On the Penon method of weakening algebraic structures
type: Item
instance of: scholarly article
title: On the Penon method of weakening algebraic structures
zbMATH Open document ID: 1003.18010
DOI: 10.1016/S0022-4049(01)00130-X
author: R. Smith
published in: Journal of Pure and Applied Algebra
publication date: 2002-08-22T00:00:00Z
review text: In the light of the author's work on defining weak \(\omega\)-categories in terms of higher operads, \textit{J. Penon} [Cah. Topologie Géom. Différ. Catégoriques 40, No.~1, 31-80 (1999; Zbl 0918.18006)] constructed a category with a forgetful functor into the category of reflexive globular sets. Penon constructs a left adjoint for that forgetful functor and calls the Eilenberg-Moore algebras for the generated monad prolixes, which he suggests are an appropriate notion of weak \(\omega\)-category. The present paper compares at a deep level (although there is still an open problem), the Penon notion with the author's notion. In an appendix, an error in the paper of \textit{M. A. Batanin} [in: Higher category theory (Evanston, IL, 1997), Contemp. Math. 230, 37-57 (1998; Zbl 0932.18004)] is corrected; techniques of that paper are fundamental here.
Mathematics Subject Classification ID: 18D20
Mathematics Subject Classification ID: 18D05
Mathematics Subject Classification ID: 18D50
zbMATH DE Number: 1787459
zbMATH Keywords: operad
zbMATH Keywords: weak n-category
zbMATH Keywords: globular set
reviewed by: Ross H. Street
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1787459