Campus Announcements

Eugenia Cheng, School of Mathematics and Statistics, University of Sheffield

Mathematics Talk: Categorification

Thursday, December 3, 2015, 4:10 p.m., Physics 123 

This week's speaker was a recent guest on The Late Show with Stephen Colbert: http://www.eater.com/2015/11/5/9674522/stephen-colbert-science-of-food-eugenia-cheng

Categorification may be thought of as the general process of adding taking a theory of something and making a higher-dimensional version.  The aim is to express greater subtleties and more closely model the higher-dimensional structures that appear in various branches of modern mathematics including homotopy theory, cohomology, K-theory, sheaves, topological quantum field theory, as well as in theoretical physics and theoretical computer science.

Category theory provides a framework for the process of categorification, but it is not straightforward or canonical.  In this talk we will compare and contrast two methods: enrichment, in which the morphisms of a category are equipped with extra structure, and internalisation, in which the entire category is computed inside another one.  We will briefly show how these methods work and how they diverge from one another by examining how they have been applied to vector spaces by Kapranov-Voevodsky, Baez and Baez-Crans.

While some familiarity with category theory will of course be useful, we will not actually assume any.

All are welcome.  Free and open to the public.  Refreshment will be provided. 

Mathematics Department                                   

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