On the subdivision of small categories

Details On the subdivision of small categories On the subdivision of small categories

2007-07-11

arxiv.org/abs/0707.1718v2

Topology and its Applications, Vol. 155, Iss. 11 (2008) 1189-1200

Mathematics

Algebraic Topology

15 pages

Scientific paper

We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of spaces and small categories, by using partially ordered sets. This yields a new conceptual proof to the well-known fact that these two homotopy categories are equivalent.

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