Weak units and homotopy 3-types
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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.
Original language | English |
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Title of host publication | CATEGORIES IN ALGEBRA, GEOMETRY AND MATHEMATICAL PHYSICS |
Editors | A Davydov, M Batanin, M Johnson, S Lack, A Neeman |
Number of pages | 20 |
Publisher | AMER MATHEMATICAL SOC |
Publication date | 2007 |
Pages | 257-276 |
ISBN (Print) | 978-0-8218-3970-6 |
Publication status | Published - 2007 |
Externally published | Yes |
Event | Conference on Categories in Algebra, Geometry and Mathematical Physics held in Honor of Ross Streets 60th Birthday - Sydney, Australia Duration: 11 Jul 2005 → 16 Jul 2005 |
Conference
Conference | Conference on Categories in Algebra, Geometry and Mathematical Physics held in Honor of Ross Streets 60th Birthday |
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Land | Australia |
By | Sydney |
Periode | 11/07/2005 → 16/07/2005 |
Series | Contemporary Mathematics |
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Volume | 431 |
ISSN | 0271-4132 |
- higher categories, weak units, braided monoidal categories, homotopy 3-types
Research areas
ID: 331502357