Category of topological spaces

The category of topological spaces is the category where each object is a topological space and each morphism is a continuous map. #m/def/topology

Well defined category

Composition of continuous maps yields a continuous map
The identity is always continuous
Function composition is already associative

Properties

Universal constructions

The initial object of is with the unique topology
The terminal object of is with the unique topology

Morphisms

Regular monomorphisms in

Naïve homotopy category is the Quotient category of with Homotopy of maps.

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