An introduction to the theory of derivators
Event details
| Date | 16.11.2012 |
| Hour | 14:15 › 15:30 |
| Speaker | Moritz Groth (Nijmegen) |
| Location |
MA 10
|
| Category | Conferences - Seminars |
The theory of derivators --going back to Grothendieck and Heller-- is a purely (2-)categorical approach to axiomatic homotopy theory. It adresses the problem that the rather crude passage from model categories to homotopy categories results in a serious loss of information. In the stable context, the typical defects of triangulated categories (non-functoriality of cone construction, lack of homotopy colimits) can be seen as a reminiscent of this fact.
The basic idea behind a derivator is that it forms homotopy categories of 'all' diagram categories and also encodes the calculus of homotopy Kan extensions.
The aim of this talk is to give an introduction to derivators and to (hopefully) advertise them as a convenient, 'weakly terminal' approach to axiomatic homotopy theory. We will see that there is a threefold hierarchy of such structures, namely derivators, pointed derivators, and stable derivators. A nice fact about this theory is that 'stability' is a property of a derivator as opposed to being an additional structure.
The basic idea behind a derivator is that it forms homotopy categories of 'all' diagram categories and also encodes the calculus of homotopy Kan extensions.
The aim of this talk is to give an introduction to derivators and to (hopefully) advertise them as a convenient, 'weakly terminal' approach to axiomatic homotopy theory. We will see that there is a threefold hierarchy of such structures, namely derivators, pointed derivators, and stable derivators. A nice fact about this theory is that 'stability' is a property of a derivator as opposed to being an additional structure.
Links
Practical information
- Informed public
- Free
Organizer
- Kathryn Hess (EPFL)