Topological category

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 $A$ along with a grounding functor $T:A\to X$ that maps to the category of sets $X$ such that $A$ admits weak or initial structures with respect to $T$. This means that constant functions in $X$ lift to $A$-morphisms and that fibers $T^{-1}x,x\in X$ are small (they are sets and not proper classes).

See also

• Infinity category
• Simplicial category

References

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