# Some proposals for the set-theoretic foundation of Category Theory

## Lorenzo Malatesta

(University of Strathclyde, Glasgow)

The problem of finding proper set-theoretic foundations for category theory has challenged mathematicians since the very beginning. In this talk we will survey some of the standard approaches that have been proposed in the past 70 years. By means of the central notions of class and universe we will sketch a possible conceptual recasting of these

proposals.

We will focus on the intended semantics for the (problematic) notion of large category in each proposed foundation. Following Feferman, we will give a comparison and evaluation of their expressive power.

**Friday 21st October 2011, 14:00**

Board Room

Department of Computer Science