A study of Kock's fat Delta
Abstract
Motivated by the study of weak identity structures in higher category theory we explore the fat Delta category, a modification of the simplex category introduced by J. Kock and provide a comprehensive study via the theory of monads with arities. Specifically, by proving that the free relative semicategory monad is strongly cartesian and identifying a dense generator, the theory of monads with arities immediately gives rise to the nerve theorem. We characterise the essential image of the nerve via the Segal condition, and show that fat Delta possesses an active-inert factorisation system. Building on these results, we also establish an isomorphism between two presentations of fat Delta.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Algebraic structures and combinatorial models
Finite Group Theory Research
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Volume
- 230
- Issue
- 11
- Pages
- 108368–108368
- Publication date
- 5 August 2026
- Language
- EN