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.
Read more about this topic: Category Of Topological Spaces
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“All cultural change reduces itself to a difference of categories. All revolutions, whether in the sciences or world history, occur merely because spirit has changed its categories in order to understand and examine what belongs to it, in order to possess and grasp itself in a truer, deeper, more intimate and unified manner.”
—Georg Wilhelm Friedrich Hegel (1770–1831)