Homomorphisms of higher categories
Abstract
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2008
- DOI:
- 10.48550/arXiv.0810.4450
- arXiv:
- arXiv:0810.4450
- Bibcode:
- 2008arXiv0810.4450G
- Keywords:
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- Mathematics - Category Theory;
- Mathematics - Algebraic Topology;
- 18D05;
- 55U35
- E-Print:
- 40 pages