A criterion for existence of right‐induced model structures. Issue 2 (3rd February 2019)

• Record Type: Journal Article
• Authors: Drummond‐Cole, Gabriel C.; Hackney, Philip
• Is Part Of: Bulletin of the London Mathematical Society. Volume 51:Issue 2(2019)
• Page Start: 309
• Page End: 326
• Publication Date: 2019-02-03
• Subjects: 55U35 -- 18A40 (primary) -- 18F20 -- 55U10 -- 18D50 (secondary); Mathematics -- Periodicals; 510
• DOI: 10.1112/blms.12232
• Languages: English
• ISSNs: 0024-6093

Abstract

Abstract: Suppose that F : N → M is a functor whose target is a Quillen model category. We give a succinct sufficient condition for the existence of the right‐induced model category structure on N in the case when F admits both adjoints. We give several examples, including change‐of‐rings, operad‐like structures, and anti‐involutive structures on infinity categories. For the last of these, we explore anti‐involutive structures for several different models of ( ∞, 1 ) ‐categories and show that known Quillen equivalences between base model categories lift to equivalences.