[[!redirects representably concrete categories]] #Contents# * table of contents {:toc} ## Definition ## A representably concrete category $C$ is a [[concrete category]] such that there exists an object $S:Ob(C)$ such that for morphisms $f:Hom(A,B)$ and $g:Hom(A,B)$, if $f \circ x = g \circ x$ for all morphisms $x:Hom(S,A)$, then $f = g$. ## See also ## * [[concrete precategory]] * [[concrete category]]