https://cattheory.subwiki.org/w/index.php?action=history&feed=atom&title=Full_functor 2026-04-08T05:49:57Z Revision history for this page on the wiki MediaWiki 1.41.2 https://cattheory.subwiki.org/w/index.php?title=Full_functor&diff=15&oldid=prev 2008-12-09T00:41:39Z

<p>New page: {{functor property}} ==Definition== ===Symbol-free definition=== A &#039;&#039;&#039;full functor&#039;&#039;&#039; is a <a href="/wiki/Functor" title="Functor">functor</a> such that the induced mapping on the collection of morphisms between any two objec...</p> <p><b>New page</b></p><div>{{functor property}}<br /> <br /> ==Definition==<br /> <br /> ===Symbol-free definition===<br /> <br /> A &#039;&#039;&#039;full functor&#039;&#039;&#039; is a [[functor]] such that the induced mapping on the collection of morphisms between any two objects is surjective.<br /> <br /> ===Definition with symbols===<br /> <br /> Suppose &lt;math&gt;\mathcal{F}:\mathcal{C} \to \mathcal{D}&lt;/math&gt; is a [[functor]] between two [[category|categories]]. &lt;math&gt;\mathcal{F}&lt;/math&gt; is termed &#039;&#039;&#039;full&#039;&#039;&#039; if for any &lt;math&gt;A,B \in \operatorname{Ob}\mathcal{C}&lt;/math&gt;, the induced map &lt;math&gt;\mathcal{F}: \mathcal{C}(A,B) \to \mathcal{D}(FA,FB)&lt;/math&gt; is surjective.<br /> <br /> ==Relation with other properties==<br /> <br /> ===Related properties===<br /> <br /> * [[Essentially surjective functor]]<br /> * [[Faithful functor]]</div>

Vipul