# On Harold Simmons's Theory of Lax Limits

## Achim Jung

(University of Birmingham)

In 1993 Harold Simmons wrote a beautiful paper on the structure and properties of lax limits in ordered categories ("The Glueing Construction and Lax Limits"). As a consequence of this theory, a new explanation of the celebrated "limit-colimit coincidence" in categories of semantic domains can be given. Together with my student Paola Maneggia we recently found that the lax limit construction can also give more insight into models of second-order lambda calculi.

In the talk I will present a brief introduction to the theory of domain equations and how they are solved in categories of semantic domains. I will explain the significance of the limit-colimit construction and then show how it follows from the theory of lax limits. Finally, I will apply the lax limit construction to models of System F (the second-order lambda calculus).

Although this abstract contains many "big words" I intend to present the ideas in a self-contained fashion so that they may be appreciated by graduate students working in any field of Theoretical Computer Science.

**Tuesday 26th September 2000, 14:00**

Robert Recorde Room

Department of Computer Science