Baez-Dolan stabilization via (semi-)model categories of operads

David White; Michael Batanin

doi:10.1007/978-3-319-45441-2_31

Baez-Dolan stabilization via (semi-)model categories of operads

David White^*, Michael Batanin

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

2 Citations (Scopus)

Abstract

We describe a proof of the Baez-Dolan Stabilization Hypothesis for Rezk's model of weak n-categories. This proof proceeds via abstract homotopy theory, and en route we discuss a version of left Bousfield localization which does not require left properness. We also discuss conditions under which various categories of operads can be made left proper, but these conditions are difficult to be satisfied, as a counterexample in the context of simplicial sets demonstrates.

Original language	English
Title of host publication	Extended abstracts Spring 2015
Subtitle of host publication	interactions between representation theory, algebraic topology and commutative algebra
Editors	Dolors Herbera, Wolfgang Pitsch, Santiago Zarzuela
Place of Publication	Cham, Switzerland
Publisher	Birkhäuser
Pages	175-179
Number of pages	5
ISBN (Print)	9783319454405
DOIs	https://doi.org/10.1007/978-3-319-45441-2_31
Publication status	Published - 2016

Publication series

Name	Trends in mathematics : research perspectives CRM Barcelona
Publisher	Birkhäuser
ISSN (Print)	2297-0215

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10.1007/978-3-319-45441-2_31

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White, D., & Batanin, M. (2016). Baez-Dolan stabilization via (semi-)model categories of operads. In D. Herbera, W. Pitsch, & S. Zarzuela (Eds.), Extended abstracts Spring 2015: interactions between representation theory, algebraic topology and commutative algebra (pp. 175-179). (Trends in mathematics : research perspectives CRM Barcelona). Birkhäuser. https://doi.org/10.1007/978-3-319-45441-2_31

White, David ; Batanin, Michael. / Baez-Dolan stabilization via (semi-)model categories of operads. Extended abstracts Spring 2015: interactions between representation theory, algebraic topology and commutative algebra. editor / Dolors Herbera ; Wolfgang Pitsch ; Santiago Zarzuela. Cham, Switzerland : Birkhäuser, 2016. pp. 175-179 (Trends in mathematics : research perspectives CRM Barcelona).

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title = "Baez-Dolan stabilization via (semi-)model categories of operads",

abstract = "We describe a proof of the Baez-Dolan Stabilization Hypothesis for Rezk's model of weak n-categories. This proof proceeds via abstract homotopy theory, and en route we discuss a version of left Bousfield localization which does not require left properness. We also discuss conditions under which various categories of operads can be made left proper, but these conditions are difficult to be satisfied, as a counterexample in the context of simplicial sets demonstrates.",

author = "David White and Michael Batanin",

year = "2016",

doi = "10.1007/978-3-319-45441-2\_31",

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White, D & Batanin, M 2016, Baez-Dolan stabilization via (semi-)model categories of operads. in D Herbera, W Pitsch & S Zarzuela (eds), Extended abstracts Spring 2015: interactions between representation theory, algebraic topology and commutative algebra. Trends in mathematics : research perspectives CRM Barcelona, Birkhäuser, Cham, Switzerland, pp. 175-179. https://doi.org/10.1007/978-3-319-45441-2_31

Baez-Dolan stabilization via (semi-)model categories of operads. / White, David; Batanin, Michael.
Extended abstracts Spring 2015: interactions between representation theory, algebraic topology and commutative algebra. ed. / Dolors Herbera; Wolfgang Pitsch; Santiago Zarzuela. Cham, Switzerland: Birkhäuser, 2016. p. 175-179 (Trends in mathematics : research perspectives CRM Barcelona).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Baez-Dolan stabilization via (semi-)model categories of operads

AU - White, David

AU - Batanin, Michael

PY - 2016

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N2 - We describe a proof of the Baez-Dolan Stabilization Hypothesis for Rezk's model of weak n-categories. This proof proceeds via abstract homotopy theory, and en route we discuss a version of left Bousfield localization which does not require left properness. We also discuss conditions under which various categories of operads can be made left proper, but these conditions are difficult to be satisfied, as a counterexample in the context of simplicial sets demonstrates.

AB - We describe a proof of the Baez-Dolan Stabilization Hypothesis for Rezk's model of weak n-categories. This proof proceeds via abstract homotopy theory, and en route we discuss a version of left Bousfield localization which does not require left properness. We also discuss conditions under which various categories of operads can be made left proper, but these conditions are difficult to be satisfied, as a counterexample in the context of simplicial sets demonstrates.

UR - https://www.scopus.com/pages/publications/85007385053

U2 - 10.1007/978-3-319-45441-2_31

DO - 10.1007/978-3-319-45441-2_31

M3 - Chapter

AN - SCOPUS:85007385053

SN - 9783319454405

T3 - Trends in mathematics : research perspectives CRM Barcelona

SP - 175

EP - 179

BT - Extended abstracts Spring 2015

A2 - Herbera, Dolors

A2 - Pitsch, Wolfgang

A2 - Zarzuela, Santiago

PB - Birkhäuser

CY - Cham, Switzerland

ER -

White D, Batanin M. Baez-Dolan stabilization via (semi-)model categories of operads. In Herbera D, Pitsch W, Zarzuela S, editors, Extended abstracts Spring 2015: interactions between representation theory, algebraic topology and commutative algebra. Cham, Switzerland: Birkhäuser. 2016. p. 175-179. (Trends in mathematics : research perspectives CRM Barcelona). doi: 10.1007/978-3-319-45441-2_31

Baez-Dolan stabilization via (semi-)model categories of operads

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