A homotopy-theoretic universal property of Leinster's operad for weak -categories

Richard Garner

doi:10.1017/S030500410900259X

A homotopy-theoretic universal property of Leinster's operad for weak -categories

Richard Garner^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

18 Downloads (Pure)

Abstract

We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak -categories, showing that the universal and canonical cofibrant replacement of the operad for strict -categories is precisely Leinster's operad for weak -categories.

Original language	English
Pages (from-to)	615-628
Number of pages	14
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	147
Issue number	3
DOIs	https://doi.org/10.1017/S030500410900259X
Publication status	Published - Nov 2009
Externally published	Yes

Bibliographical note

Copyright [2009] Cambridge Philosophical Society. Published by Cambridge University Press. Article originally published in [Garner R. "A Homotopy-theoretic universal property of Leinster's operad for weak Ï‰-categories." Math. Proc. Camb. Phil. Soc. (2009), 147, 615]. The original article can be found at [http://dx.doi.org/10.1017/S030500410900259X].

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author = "Richard Garner",

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AB - We explain how any cofibrantly generated weak factorisation system on a category may be equipped with a universally and canonically determined choice of cofibrant replacement. We then apply this to the theory of weak -categories, showing that the universal and canonical cofibrant replacement of the operad for strict -categories is precisely Leinster's operad for weak -categories.

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A homotopy-theoretic universal property of Leinster's operad for weak -categories

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