Homomorphisms of higher categories

Details Homomorphisms of higher categories Homomorphisms of higher categories

2008-10-24

arxiv.org/abs/0810.4450v3

Advances in Mathematics 224 (2010), no. 6, pages 2269-2311

Mathematics

Category Theory

40 pages; v2: hand-waving arguments replaced by proofs; v3: final journal version

Scientific paper

10.1016/j.aim.2010.01.022

We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction is such that these homomorphisms admit a strictly associative and unital composition. We give two applications of this construction. The first is to tricategories; and here we do not obtain the trihomomorphisms defined by Gordon, Power and Street, but only something equivalent in a suitable sense. The second is to Batanin's weak omega-categories.

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