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Weak units and homotopy 3-types

By André Joyal and Joachim Kock

Street Festschrift: Categories in algebra, geometry and mathematical physics,
Contemp. Math 431 (2007), 257-276.

ArXiv:math.CT/0602084.

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.

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Last updated: 2007-07-02 by Joachim Kock.