= Morphism in a category
{title2=$f:A\to B$}
= Categorical morphism
{synonym}
A <categorical morphism> is an arrow with a specified source and target in a <category>. An arrow $f:A\to B$ composes with $g:B\to C$ to give $gf:A\to C$. Composition is associative, and every object has an identity arrow acting as a unit. A <functor> preserves the sources, targets, identities and compositions of these arrows. In a <locally small category>, the arrows between fixed objects form a <hom-set>.
Back to article page
