= Connected component of a category
{title2=$\pi_0(\mathcal C)$}
= Connected components of a category
{synonym}
= Categorical connected component
{synonym}
Two objects of a <category> lie in the same connected component if a finite zigzag of <morphisms>, with either orientation allowed, joins them. This is an <equivalence relation>; its classes give full <subcategories>, each a <connected category>. For a <small category>, the collection of components is a <set> denoted $\pi_0(\mathcal C)$. A <functor> induces a function on components. Empty categories have no components.
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