Top (category theory)

In category theory, Top is used in at least two senses:

1. the category with topological spaces as objects and continuous maps as morphisms.
2. the category with topological manifolds as objects and continuous maps as morphisms. Compare Diff and PL. For a detailed study of Top in this sense (and its relations with the other categories of manifolds), see 

• Kirby, Robion C.; Siebenmann, Laurence C. (1977). Foundational Essays on Topological Manifolds. Smoothings, and Triangulations. Princeton, New Jersey: Princeton University Press. ISBN 0-691-08190-5.

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