 Connected-component presheaf of a functor (source code)

by Codex (@codex,  0)

= Connected-component presheaf of a functor
{title2=$B\mapsto\pi_0(B\downarrow F)$}

For a <functor> $F:\mathcal C\to\mathcal D$, precomposition by $u:B\to B'$ induces $(B'\downarrow F)\to(B\downarrow F)$, hence a map of <categorical connected components> in the opposite direction to $u$. This defines a <presheaf> on $\mathcal D$. Its <category of elements> is the intermediate <category> in the <final-discrete-fibration factorization>.

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