97th Peripatetic Seminar
on Sheaves and Logic,
Université Catholique de Louvain,
31 January 2015.
Abstract It was Steve Schanuel who established that the right way to "count" a topological space is to take its Euler characteristic -- that Euler characteristic is to spaces what cardinality is to sets. Pursuing his insight leads to a general definition of the Euler characteristic, or magnitude, of a (suitably finite) enriched category. Different choices of base category produce cardinality-like invariants in different branches of mathematics. I will describe what happens over Vect. In particular, every associative algebra A gives rise canonically to a certain Vect-enriched category, which in turn has an Euler characteristic; and as I will show, this is a recognizable homological invariant of A. This invariant perhaps deserves to be known as the Euler characteristic of an associative algebra.
Slides In this pdf file.