Nerves and classifying spaces for bicategories

Details Nerves and classifying spaces for bicategories Nerves and classifying spaces for bicategories

2009-03-30

arxiv.org/abs/0903.5058v1

Mathematics

Algebraic Topology

42 pages

Scientific paper

This paper explores the relationship amongst the various simplicial and pseudo-simplicial objects characteristically associated to any bicategory C. It proves the fact that the geometric realizations of all of these possible candidate `nerves of C' are homotopy equivalent. Any one of these realizations could therefore be taken as the classifying space BC of the bicategory. Its other major result proves a direct extension of Thomason's `Homotopy Colimit Theorem' to bicategories: When the homotopy colimit construction is carried out on a diagram of spaces obtained by applying the classifying space functor to a diagram of bicategories, the resulting space has the homotopy type of a certain bicategory, called the `Grothendieck construction on the diagram'. Our results provide coherence for all reasonable extensions to bicategories of Quillen's definition of the `classifying space' of a category as the geometric realization of the category's Grothendieck nerve, and they are applied to monoidal (tensor) categories through the elemental `delooping' construction.

Affiliated with

Also associated with

No associations

Rating

Nerves and classifying spaces for 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 Nerves and classifying spaces for bicategories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nerves and classifying spaces for bicategories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-424227