# An Introduction to Dilators

#### 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

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