# Egbert Rijke: Group theory in univalent mathematics

Source: Mathematics and theoretical computing seminar

**Pozor: dobimo se ob nestandardnem času na nestandardnem mestu, ov 13:15 v 2.04!**

**Attention: we meet at a non-standard time and place at 13:15 in 2.04!**

Egbert Rijke, University of Illinois at Urbana-Champaign, USA

**Abstract:** The univalence axiom allows us to identify isomorphic groups. This is common practice, even though it is inconsistent with set theory. In the first half of the seminar, we show how to do this. In the second half of the seminar we turn to a different presentation of the category of groups, where the objects are pointed connected groupoids. This looks more like the category one would use for the theory of covering spaces. We will show how to develop some of the basic concepts of group theory in this equivalent (and hence equal) category of groups.