# An Introduction to Dilators

**Date**: Wednesday 10 May 2017, 14:00 – 15:30**Location**: Mathematics Level 8, MALL 1 & 2, School of Mathematics**Type**: Pure Mathematics seminars, Proofs, constructions and computations seminars, Seminar series**Cost**: Free

#### Anton Freund, University of Leeds. Part of the proofs, constructions and computations seminar series.

Dilators, due to Girard, are functors from well-orders to well-orders that preserve direct limits and pull-backs. Having explained this definition I will focus on two basic facts: Firstly, preservation of direct limits and pull-backs is equivalent to the existence of a unique natural transformation which computes finite "supports". Secondly, a dilator (which is a class-sized object) is completely determined by its (set-sized) restriction to the natural numbers.

**Anton Freund,** *University of Leeds*