23 September 2008
2:30 - 4:00 Victor Harnik
Computads and multitopic sets: two ways of specifying
cells in higher dimensional categories
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.