Category theory is a relatively new branch of mathematics which seeks to understand abstract mathematical structure. At its core, category theory contains a synthesis of algebraic, logical and geometric intuitions. This allows for both diverse applications and innovative insights in areas including pure mathematics, computer science, physics etc. The Scottish Category Theory Seminar provides a forum for discussion of all aspects of category, be they straight category theory or applications to other scientific fields.
Our seventh meeting takes place on Friday 8 February 2013 at the International Centre for Mathematical Sciences, in the centre of Edinburgh (15 South College St; map). We intend the meeting to be attractive to mathematicians, computer scientists, physicists etc., and thus aim for talks of interest to a broad audience of people interested in category theory.
This meeting is generously supported by the Glasgow Mathematical Journal Learning and Research Support Fund.
We construct a sheaf-based model in which all functions from the Cantor space to the natural numbers are uniformly continuous. Our development of the model is constructive, and has been carried out in intensional type theory in Agda notation. In particular, this gives computational content to constructive proofs that use the uniform continuity axiom.
If C is a bicomplex of abelian groups then there are two ways in which one can extract an ordinary complex: one can either form the total complex Tot(C), or one can form the diagonal complex d(C). The Eilenberg–Zilber theorem states that these two complexes are quasi-isomorphic. There is a generalization of this theorem at the level of simplicial sets: if X is a bisimplicial set then there are two ways in which one can extract a simplicial set from X, the diagonal and the total simplicial set constructions. It is a theorem, due to Cegarra and Remedios, and independently Joyal and Tierney, that these two simplicial sets are weakly homotopy equivalent. The aim of this talk is to describe a simple proof of this theorem.
Blog post related to Willerton's talk.
If you intend to come to the meeting, it would be helpful (but is not essential) to drop us a one-line email beforehand.
Email: Tom.Leinster#ed.ac.uk (changing # to @).
Organizers: Neil Ghani, Tom Leinster (local organizer), Alex Simpson.
This page was last changed on 11 February 2013.