The usual definition of associativity simply states that (ab)c = a(bc)
holds for any triple a, b, and c. However, when we use associativity
in practice, often our products have more than three factors. When one
is working in a context where the natural notion of sameness is not that
of equality, this discrepancy becomes a serious issue and one is forced
to consider "higher" associativity. (For example, the fundamental group
of a topological space enjoys a shadow of this sort of associativity.)
In this talk, I will explain how category theory may be used to deal
with such "higher" algebra.