### Cohomology and Computation (Week 21)

#### Posted by John Baez

This time in our course on Cohomology and Quantization we explained why mathematicians like to turn algebraic gadgets and topological spaces into simplicial sets — and how this actually works, in the case of topological spaces:

- Week 21 (Apr. 19) - Simplicial sets and cohomology. Two sources of simplicial sets: topology and algebra. The topologist’s category of simplices, $\Delta_{top}$. How a topological space $X$ gives a simplicial set called its ‘singular simplicial set’ $S X$. How this gives a functor $S: Top \to SimpSet$.

Last week’s notes are here; next week’s notes are here.

There won’t be any class on Tuesday the 24th or Thursday the 26th. I’ll be in France! I’m giving a talk at this workshop:

- Philosophical and Formal Foundations of Modern Physics, at the Fondation des Treilles, April 23-28, 2007. Organized by Michel Bitbol and Alexei Grinbaum.

The other people attending are: Howard Barnum, Katherine Brading, Jeffrey Bub, Brigitte Falkenburg, Michael Friedman, Lucien Hardy, Patricia Kauark-Leite, Marc Lachieze-Rey, Hermann Nicolai, Paolo Parrini, Jean Petitot, Oliver Pooley, Thomas Ryckman, Matteo Smerlak, Rob Spekkens, Paul Teller, and Christopher Timpson.

My talk will be related to some earlier themes of this class. You can see it here:

It’s a lot like the talk I gave at the Perimeter Institute last spring, but with less physics, more philosophy, nothing on higher categories, and a bit on spans and cospans.

On the way back I’ll spend a day in Nice talking to Eugenia Cheng.

## Re: Cohomology and Computation (Week 21)

The construction of a simplicial set for groups, rings, Lie algebras, etc. – does that have a name? I’ve always suspected something like that existed, but I don’t know what to look for.