Homomorphisms of higher categories
Category Theory
2011-10-17 v3 Algebraic Topology
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.
Cite
@article{arxiv.0810.4450,
title = {Homomorphisms of higher categories},
author = {Richard Garner},
journal= {arXiv preprint arXiv:0810.4450},
year = {2011}
}
Comments
40 pages; v2: hand-waving arguments replaced by proofs; v3: final journal version