A quillen model structure for 2-categories

Stephen Lack*

*Corresponding author for this work

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We describe a cofibrantly generated Quillen model structure on the locally finitely presentable category 2-Cat of (small) 2-categories and 2-functors; the weak equivalences are the biequivalences, and the homotopy relation on 2-functors is just pseudonatural equivalence. The model structure is proper, and is compatible with the monoidal structure given by the Gray tensor product. It is not compatible with the Cartesian closed structure, in which the tensor product is the product. The model structure restricts to a model structure on the full subcategory PsGpd of 2-Cat, consisting of those 2-categories in which every arrow is an equivalence and every 2-cell is invertible. The model structure on PsGpd is once again proper, and compatible with the monoidal structure given by the Gray tensor product.

Original languageEnglish
Pages (from-to)171-205
Number of pages35
JournalK-Theory: interdisciplinary journal for the development, application and influence of K-theory in the mathematical sciences
Volume26
Issue number2
DOIs
Publication statusPublished - 2002
Externally publishedYes

Keywords

  • 2-category
  • Biequivalence
  • Gray tensor product
  • Quillen model category

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