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
Famous quotes containing the word categories:
“Of course I’m a black writer.... I’m not just a black writer, but categories like black writer, woman writer and Latin American writer aren’t marginal anymore. We have to acknowledge that the thing we call “literature” is more pluralistic now, just as society ought to be. The melting pot never worked. We ought to be able to accept on equal terms everybody from the Hassidim to Walter Lippmann, from the Rastafarians to Ralph Bunche.”
—Toni Morrison (b. 1931)