Homomorphisms of higher categories

Richard Garner*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)


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 languageEnglish
Pages (from-to)2269-2311
Number of pages43
JournalAdvances in Mathematics
Issue number6
Publication statusPublished - Aug 2010
Externally publishedYes


  • Abstract homotopy theory
  • Higher-dimensional categories
  • Weak morphisms

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