We will continue online on Thursday, October 15th, at 1pm on ZOOM platform (for information how to acces seminar and next programme visit this page) by the talk:

Taichi Uemura

The universal exponentiable arrow

Abstract:
Cartmell showed that the category of generalized algebraic theories is equivalent to the category of contextual categories. This implies that the theory of generalized algebraic theories is essentially algebraic. We characterize the essentially algebraic theory of generalized algebraic theories as the free category with finite limits and with an exponentiable arrow.

The main theorem and a syntactic proof are found in arXiv:2001.09940. In this talk we give a semantic proof.