23 September 2008

2:30 - 4:00   Victor Harnik
Computads and multitopic sets: two ways of specifying cells in higher dimensional categories

Abstract:
Given a collection of cells in a higher dimensional category, we have two formal languages in which we can describe other cells that can be obtained from them with the help of composition operations. One, based on the ordinary composition operations, can describe all such cells. The other, based on the so called placed composition operations, seems preferable in some respects, but can describe only some such cells. When made into free mathematical structures, these languages become computads and multitopic sets and can be compared to each other.
The subject is relevant to the problem of defining the concept of weak higher dimensional category.