Topology MOC

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. 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 the category of topological spaces

Related categories

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

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