Skew structures in 2-category theory and homotopy theory

John Bourke*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Citations (Scopus)


We study Quillen model categories equipped with a monoidal skew closed structure that descends to a genuine monoidal closed structure on the homotopy category. Our examples are 2-categorical and include permutative categories and bicategories. Using the skew framework, we adapt Eilenberg and Kelly’s theorem relating monoidal and closed structure to the homotopical setting. This is applied to the construction of monoidal bicategories arising from the pseudo-commutative 2-monads of Hyland and Power.

Original languageEnglish
Pages (from-to)31-81
Number of pages51
JournalJournal of Homotopy and Related Structures
Issue number1
Publication statusPublished - 1 Mar 2017
Externally publishedYes


  • skew monoidal category
  • quillen model category
  • 2-category

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