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 rather something which is equivalent in a suitable sense. The second application is to Batanin's weak ω-categories.
Original language | English |
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Pages (from-to) | 2269-2311 |
Number of pages | 43 |
Journal | Advances in Mathematics |
Volume | 224 |
Issue number | 6 |
DOIs | |
Publication status | Published - Aug 2010 |
Externally published | Yes |
Keywords
- Abstract homotopy theory
- Higher-dimensional categories
- Weak morphisms