Weak units and homotopy 3-types

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Standard

Weak units and homotopy 3-types. / Joyal, Andre; Kock, Joachim.

CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS. red. / A Davydov; M Batanin; M Johnson; S Lack; A Neeman. AMER MATHEMATICAL SOC, 2007. s. 257-276 (Contemporary Mathematics, Bind 431).

Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt

Harvard

Joyal, A & Kock, J 2007, Weak units and homotopy 3-types. i A Davydov, M Batanin, M Johnson, S Lack & A Neeman (red), CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS. AMER MATHEMATICAL SOC, Contemporary Mathematics, bind 431, s. 257-276, Conference on Categories in Algebra, Geometry and Mathematical Physics held in Honor of Ross Streets 60th Birthday, Sydney, Australien, 11/07/2005.

APA

Joyal, A., & Kock, J. (2007). Weak units and homotopy 3-types. I A. Davydov, M. Batanin, M. Johnson, S. Lack, & A. Neeman (red.), CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS (s. 257-276). AMER MATHEMATICAL SOC. Contemporary Mathematics Bind 431

Vancouver

Joyal A, Kock J. Weak units and homotopy 3-types. I Davydov A, Batanin M, Johnson M, Lack S, Neeman A, red., CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS. AMER MATHEMATICAL SOC. 2007. s. 257-276. (Contemporary Mathematics, Bind 431).

Author

Joyal, Andre ; Kock, Joachim. / Weak units and homotopy 3-types. CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS. red. / A Davydov ; M Batanin ; M Johnson ; S Lack ; A Neeman. AMER MATHEMATICAL SOC, 2007. s. 257-276 (Contemporary Mathematics, Bind 431).

Bibtex

@inproceedings{b4df85529fe243bab8f3df0a8c8a3e53,

title = "Weak units and homotopy 3-types",

abstract = "We show that every braided monoidal category arises as End(I) for a weak unit I in an otherwise completely strict monoidal 2-category. This implies a version of Simpson's weak-unit conjecture in dimension 3, namely that one-object 3-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy 3-types. The proof has a clear intuitive content and relies on a geometrical argument with string diagrams and configuration spaces.",

keywords = "higher categories, weak units, braided monoidal categories, homotopy 3-types",

author = "Andre Joyal and Joachim Kock",

year = "2007",

language = "English",

isbn = "978-0-8218-3970-6",

series = "Contemporary Mathematics",

publisher = "AMER MATHEMATICAL SOC",

pages = "257--276",

editor = "A Davydov and M Batanin and M Johnson and S Lack and A Neeman",

booktitle = "CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS",

note = "Conference on Categories in Algebra, Geometry and Mathematical Physics held in Honor of Ross Streets 60th Birthday ; Conference date: 11-07-2005 Through 16-07-2005",

}

RIS

TY - GEN

T1 - Weak units and homotopy 3-types

AU - Joyal, Andre

AU - Kock, Joachim

PY - 2007

Y1 - 2007

N2 - We show that every braided monoidal category arises as End(I) for a weak unit I in an otherwise completely strict monoidal 2-category. This implies a version of Simpson's weak-unit conjecture in dimension 3, namely that one-object 3-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy 3-types. The proof has a clear intuitive content and relies on a geometrical argument with string diagrams and configuration spaces.

AB - We show that every braided monoidal category arises as End(I) for a weak unit I in an otherwise completely strict monoidal 2-category. This implies a version of Simpson's weak-unit conjecture in dimension 3, namely that one-object 3-groupoids that are strict in all respects, except that the object has only weak identity arrows, can model all connected, simply connected homotopy 3-types. The proof has a clear intuitive content and relies on a geometrical argument with string diagrams and configuration spaces.

KW - higher categories

KW - weak units

KW - braided monoidal categories

KW - homotopy 3-types

M3 - Article in proceedings

SN - 978-0-8218-3970-6

T3 - Contemporary Mathematics

SP - 257

EP - 276

BT - CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS

A2 - Davydov, A

A2 - Batanin, M

A2 - Johnson, M

A2 - Lack, S

A2 - Neeman, A

PB - AMER MATHEMATICAL SOC

T2 - Conference on Categories in Algebra, Geometry and Mathematical Physics held in Honor of Ross Streets 60th Birthday

Y2 - 11 July 2005 through 16 July 2005

ER -

ID: 331502357