https://cattheory.subwiki.org/w/index.php?action=history&feed=atom&title=EpimorphismEpimorphism - Revision history2026-05-05T05:55:31ZRevision history for this page on the wikiMediaWiki 1.41.2https://cattheory.subwiki.org/w/index.php?title=Epimorphism&diff=23&oldid=prevVipul: New page: {{morphism property}} ==Definition== Suppose <math>\mathcal{C}</math> is a category, <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math>. <math>f</...2008-12-09T00:53:24Z<p>New page: {{morphism property}} ==Definition== Suppose <math>\mathcal{C}</math> is a category, <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math>. <math>f</...</p>
<p><b>New page</b></p><div>{{morphism property}}<br />
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==Definition==<br />
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Suppose <math>\mathcal{C}</math> is a category, <math>A,B \in \operatorname{Ob}\mathcal{C}</math>, and <math>f \in \mathcal{C}(A,B)</math>. <math>f</math> is termed an '''epimorphism''', or '''epic''', if for any object <math>C</math> and any <math>g,h \in \mathcal{C}(B,C)</math> we have:<br />
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<math>g \circ f = h \circ f \implies g = h</math>.<br />
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==Relation with other properties==<br />
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===Stronger properties===<br />
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* [[Weaker than::Isomorphism]]<br />
* [[Weaker than::Retraction]]<br />
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===Related properties===<br />
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* [[Monomorphism]]</div>Vipul