# Topological category

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In category theory, a discipline in mathematics, a **topological category** is a category that is enriched over the category of compactly generated Hausdorff spaces. They can be used as a foundation for higher category theory.Template:Harv

A topological category is a category along with a grounding functor that maps to the category of sets such that admits weak or initial structures with respect to . This means that constant functions in lift to -morphisms and that fibers are small (they are sets and not proper classes).^{[1]}

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