### Bacard on Segal Enriched Categories

#### Posted by Tom Leinster

Hugo Bacard, a PhD student at Nice working with Carlos Simpson, has just put a new paper on the arXiv: Segal enriched categories I. It’s all about homotopy-enrichment.

The basic aim is to study categories enriched — in an up-to-homotopy way — in a bicategory equipped with a class of 2-cells to be thought of as homotopy equivalences. It’s clear from the introduction that Bacard’s formalism covers a very wide range of structures indeed. For instance, you’ll see appearances made by homotopy algebras, torsors, discrete valuation rings, metric spaces, parallel transport functors, …. Even motivic cohomology gets a mention.

The exposition looks nice. There are also some unusual and intriguing pictures. Would anyone like to have a bash at writing a short summary?

Posted at September 22, 2010 2:54 AM UTC