Classifying spaces for braided monoidal categories and lax diagrams of bicategories

Details Classifying spaces for braided monoidal categories and lax diagrams of bicategories Classifying spaces for braided monoidal categories and lax diagrams of bicategories

2009-07-06

arxiv.org/abs/0907.0930v3

Mathematics

Category Theory

This a revised version (with 59 pages now) of our paper on realizations of braided categories, where we have taken into accoun

Scientific paper

This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy type of their classifying spaces. Bicategories (in particular monoidal categories) have well understood simple geometric realizations, and we here deal with homotopy types represented by lax diagrams of bicategories, that is, lax functors to the tricategory of bicategories. In this paper, it is proven that, when a certain bicategorical Grothendieck construction is performed on a lax diagram of bicategories, then the classifying space of the resulting bicategory can be thought of as the homotopy colimit of the classifying spaces of the bicategories that arise from the initial input data given by the lax diagram. This result is applied to produce bicategories whose classifying space has a double loop space with the same homotopy type, up to group completion, as the underlying category of any given (non-necessarily strict) braided monoidal category. Specifically, it is proven that these double delooping spaces, for categories enriched with a braided monoidal structure, can be explicitly realized by means of certain genuine simplicial sets characteristically associated to any braided monoidal categories, which we refer to as their (Street's) geometric nerves.

Affiliated with

Also associated with

No associations

Rating

Classifying spaces for braided monoidal categories and lax diagrams of bicategories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Classifying spaces for braided monoidal categories and lax diagrams of bicategories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classifying spaces for braided monoidal categories and lax diagrams of bicategories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-27275