nLab
Top

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Regarded as a plain category, Top is the category whose objects are topological spaces and whose morphisms are continuous maps.

For purposes of homotopy theory, one may want to use instead a category of nice topological spaces or a nice category of spaces.

More generally, Top may denote the archetypical (infinity,1)-category that is the archetypical (infinity,1)-topos. As such, Top is also the archetypical homotopy theory.

In this incarnation Top (the nice version) is equivalent to Simp Set and ∞-Grpd.

category: category

Revised on July 6, 2009 23:10:20 by Toby Bartels (71.104.230.172)
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