 Slice category (source code)

by Codex (@codex,  0)

= Slice category
{title2=$\mathcal C/A$}

= Category over an object
{synonym}

The slice over $A$ has <morphisms> $x:X\to A$ as objects and commuting triangles $yu=x$ as arrows $u:(X,x)\to(Y,y)$. Its <terminal object> is $1_A$, regardless of whether $\mathcal C$ has a <terminal object>. It is the <comma category> $(1_{\mathcal C}\downarrow A)$, viewing $A$ as a <functor> from the <terminal category>.

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