An Isomorphism
<p> </p><ol style="margin: 0px; padding: 0px 0px 0px 2.25em; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: rgb(34, 34, 34);"><li style="margin-top: 0px; margin-right: 0px; margin-bottom: inherit; margin-left: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">Similarity of form</li></ol><dl style="margin: 0px 0px 0px 1em; padding: 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; color: rgb(34, 34, 34);"><dd style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; overflow: auto;"><ol style="margin: 0px; padding: 0px 0px 0px 2.25em; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/biology" title="biology" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">biology</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> the <a href="https://en.m.wiktionary.org/wiki/similarity" title="similarity" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">similarity</a> in <a href="https://en.m.wiktionary.org/wiki/form" title="form" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">form</a> of <a href="https://en.m.wiktionary.org/wiki/organism" title="organism" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">organisms</a>, which may be due to <a href="https://en.m.wiktionary.org/wiki/convergent_evolution" title="convergent evolution" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">convergent evolution</a> or shared genetic background, e.g. an algae species in which the <a href="https://en.m.wiktionary.org/wiki/haploid" title="haploid" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">haploid</a> and <a href="https://en.m.wiktionary.org/wiki/diploid" title="diploid" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">diploid</a> life stages are indistinguishable based on morphology.</li><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/chemistry" title="chemistry" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">chemistry</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> the similarity in the <a href="https://en.m.wiktionary.org/wiki/crystal" title="crystal" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">crystal</a>structures of similar <a href="https://en.m.wiktionary.org/wiki/chemical" title="chemical" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">chemical</a><a href="https://en.m.wiktionary.org/wiki/compound" title="compound" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">compounds</a></li><li style="margin-top: 0px; margin-right: 0px; margin-bottom: inherit; margin-left: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/sociology" title="sociology" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">sociology</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> the similarity in the structure or <a href="https://en.m.wiktionary.org/wiki/processes" title="processes" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">processes</a> of different <a href="https://en.m.wiktionary.org/wiki/organization" title="organization" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">organizations</a></li></ol></dd><dd style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; overflow: auto;"> 2. A one-to-one correspondence<ol style="margin: 0px; padding: 0px 0px 0px 2.25em; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">group algebra</span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> A <a href="https://en.m.wiktionary.org/wiki/bijection" title="bijection" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">bijection</a> <i style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">f</i> such that both <i style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">f</i> and its <a href="https://en.m.wiktionary.org/wiki/inverse_function" title="inverse function" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">inverse</a> <i style="margin: 0px; padding: 0px; border: 0px; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">f</i><sup style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: 1; font-family: inherit; font-size: 0.75em; background: none;"> −1</sup> are <a href="https://en.m.wiktionary.org/wiki/homomorphism" title="homomorphism" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">homomorphisms</a>, that is, structure-preserving mappings.</li><li style="margin: 0px 0px 10px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/computer_science" title="computer science" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">computer science</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> a <a href="https://en.m.wiktionary.org/wiki/one-to-one" title="one-to-one" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">one-to-one</a><a href="https://en.m.wiktionary.org/wiki/correspondence" title="correspondence" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">correspondence</a> between all the <a href="https://en.m.wiktionary.org/wiki/element" title="element" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">elements</a> of two <a href="https://en.m.wiktionary.org/wiki/set" title="set" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">sets</a>, e.g. the <a href="https://en.m.wiktionary.org/wiki/instance" title="instance" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">instances</a> of two <a href="https://en.m.wiktionary.org/wiki/class" title="class" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">classes</a>, or the <a href="https://en.m.wiktionary.org/wiki/record" title="record" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">records</a> in two <a href="https://en.m.wiktionary.org/wiki/dataset" title="dataset" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">datasets</a></li><li style="margin-top: 0px; margin-right: 0px; margin-bottom: inherit; margin-left: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">(</span><span class="ib-content" style="margin: 0px; padding: 0px; border: 0px; font-style: italic; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/category_theory" title="category theory" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">category theory</a></span><span class="ib-brac" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;">)</span> A <a href="https://en.m.wiktionary.org/wiki/morphism" title="morphism" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">morphism</a> which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).</li></ol></dd></dl><h4 class="in-block" style="margin: 0px; padding: 0.5em 0px; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: 1.3; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; overflow-wrap: break-word; word-break: break-word; display: table; color: rgb(34, 34, 34);"><span class="mw-headline" id="Antonyms" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: middle; background: none; display: table-cell; width: 272px;">Antonyms</span><span class="mw-editsection" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: middle; background: none; display: table-cell;"><a href="https://en.m.wiktionary.org/w/index.php?title=isomorphism&action=edit&section=6" title="Edit section: Antonyms" data-section="6" class="mw-ui-icon mw-ui-icon-element mw-ui-icon-minerva-edit-enabled edit-page" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: 1.5em; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161); position: relative; min-height: 1.5em; min-width: 3.5em; text-indent: -999px; overflow: hidden; width: 3.5em; max-width: 3.5em; display: block;">Edit</a></span></h4><ul style="margin: 0px; padding: 0px 0px 0px 1em; border: 0px; font-variant-numeric: inherit; font-variant-east-asian: inherit; font-stretch: inherit; line-height: inherit; font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Lato, Helvetica, Arial, sans-serif; vertical-align: baseline; background-image: none; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; list-style-position: initial; list-style-image: initial; color: rgb(34, 34, 34);"><li style="margin-top: 0px; margin-right: 0px; margin-bottom: inherit; margin-left: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><span class="Latn" lang="en" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none;"><a href="https://en.m.wiktionary.org/wiki/anisomorphism#English" title="anisomorphism" style="margin: 0px; padding: 0px; border: 0px; font-style: inherit; font-variant: inherit; font-weight: inherit; font-stretch: inherit; line-height: inherit; font-family: inherit; vertical-align: baseline; background: none; color: rgb(107, 75, 161);">anisomorphism</a></span></li></ul>