Weak units and homotopy 3-types
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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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
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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