# Homotopy Type Theory representably concrete category > history (Rev #2, changes)

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# Contents

## 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 $f = g$.