Category of Topological Spaces - Relationships To Other Categories

Relationships To Other Categories

  • The category of pointed topological spaces Top is a coslice category over Top.
  • The homotopy category hTop has topological spaces for objects and homotopy equivalence classes of continuous maps for morphisms. This is a quotient category of Top. One can likewise form the pointed homotopy category hTop.
  • Top contains the important category Haus of topological spaces with the Hausdorff property as a full subcategory. The added structure of this subcategory allows for more epimorphisms: in fact, the epimorphisms in this subcategory are precisely those morphisms with dense images in their codomains, so that epimorphisms need not be surjective.

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