https://cattheory.subwiki.org/w/index.php?action=history&feed=atom&title=Faithful_functorFaithful functor - Revision history2026-05-28T12:06:43ZRevision history for this page on the wikiMediaWiki 1.41.2https://cattheory.subwiki.org/w/index.php?title=Faithful_functor&diff=7&oldid=prevVipul: New page: {{functor property}} ==Definition== ===Symbol-free definition=== A functor is faithful if the induced map on the collection of morphisms between any pair of objects is injective. ===Def...2008-12-09T00:14:31Z<p>New page: {{functor property}} ==Definition== ===Symbol-free definition=== A functor is faithful if the induced map on the collection of morphisms between any pair of objects is injective. ===Def...</p>
<p><b>New page</b></p><div>{{functor property}}<br />
==Definition==<br />
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===Symbol-free definition===<br />
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A functor is faithful if the induced map on the collection of morphisms between any pair of objects is injective.<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 '''faithful''' if it is true that for any objects <math>A,B \in \mathcal{C}</math>, the induced map:<br />
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<math>\mathcal{F}: \mathcal{C}(A,B) \to \mathcal{D}(FA,FB)</math><br />
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is injective.</div>Vipul