https://cattheory.subwiki.org/w/index.php?action=history&feed=atom&title=Conservative_functorConservative functor - Revision history2026-05-22T01:43:01ZRevision history for this page on the wikiMediaWiki 1.41.2https://cattheory.subwiki.org/w/index.php?title=Conservative_functor&diff=13&oldid=prevVipul: New page: {{functor property}} ==Definition== ===Symbol-free definition=== A functor is termed '''conservative''' if it reflects isomorphisms: in other words, any morphism that gets mapped to...2008-12-09T00:37:07Z<p>New page: {{functor property}} ==Definition== ===Symbol-free definition=== A <a href="/wiki/Functor" title="Functor">functor</a> is termed '''conservative''' if it reflects isomorphisms: in other words, any morphism that gets mapped to...</p>
<p><b>New page</b></p><div>{{functor property}}<br />
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==Definition==<br />
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===Symbol-free definition===<br />
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A [[functor]] is termed '''conservative''' if it reflects isomorphisms: in other words, any morphism that gets mapped to an isomorphism must be an isomorphism to begin with.<br />
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===Definition with symbols===<br />
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Suppose <math>\mathcal{F}:\mathcal{C} \to \mathcal{D}</math> is a [[functor]] between two [[category|categories]]. We say that <math>\mathcal{F}</math> is '''conservative''' if, whenever <math>A,B \in \operatorname{Ob} \mathcal{C}</math> and <math>f \in \mathcal{C}(A,B)</math> such that <math>Ff</math> is an isomorphism from <math>FA</math> to <math>FB</math>, <math>f</math> is an isomorphism.<br />
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==Relation with other properties==<br />
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===Stronger properties===<br />
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* [[Weaker than::Strongly conservative functor]]</div>Vipul