Weakly ω-Categorified Models of Algebraic Theories

2020/06/26 by Bressie, Phillip M, Yetter, David N
#18C10 #18M90 #18N25 #20N99 #Category Theory (math.CT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.15188

Abstract

We provide the expected constructions of weakly ω-categorified models (in the sense of Bressie) of the theory of groups and quandles which arise by replacing the homotopies used to give equivalence relations in the theory of fundamental groups, fundamental quandles, and knot quandles with homotopies of all orders used as arrows of categorical dimensions one and greater, and discuss other related constructions of weakly ω-categorifed algebras.

Related

• Weak model categories in classical and constructive mathematics
• Globular weak \ω-categories as models of a type theory
• Algebraic models of homotopy types and the homotopy hypothesis
• The homotopy relation in a category with weak equivalences
• A folk model structure on omega-cat