Timothy Porter (University of Wales, Bangor, UK), Rewriting and Homotopy
Schedule
- Feb. 27, 2012, 9:00 - 10:30
- Feb. 28, 2012, 11:00 - 12:30
- March 1, 2012, 9:00 - 10:30
- March 2, 2012, 11:00 - 12:30
Abstract
I. & II. Some combinatorial group theory and low dimensional homotopy: Presentations, identities among relations, crossed modules, and crossed resolutions. Homological and homotopical syzygies. Higher generation by subgroups (Abels and Holz). Examples.
III. An introduction to homotopy coherence and its rewriting aspect. Homotopy coherence and the resolution of a category. Examples of homotopy coherent diagrams and the homotopy coherent nerve. Quasi-categories. The link with rewriting.
IV. How to adapt away from the group theory case... brief discussion of directed homotopy, polygraphs etc. and how to work with rewriting and syzygies in the non-group case, some pointers to combinatorial category theory.
Attachments
I. & II. Some combinatorial group theory and low dimensional homotopy: Presentations, identities among relations, crossed modules, and crossed resolutions. Homological and homotopical syzygies. Higher generation by subgroups (Abels and Holz). Examples.
III. An introduction to homotopy coherence and its rewriting aspect. Homotopy coherence and the resolution of a category. Examples of homotopy coherent diagrams and the homotopy coherent nerve. Quasi-categories. The link with rewriting.
IV. How to adapt away from the group theory case... brief discussion of directed homotopy, polygraphs etc. and how to work with rewriting and syzygies in the non-group case, some pointers to combinatorial category theory.