Time：16:00-17:00, Tuesday, October 27, 2026
Venue：E14-301
Speaker：Laurent Lafforgue, Lagrange Centre
Title：On presheaf-type theories
Abstract：A geometric first-order theory is called a "presheaf-type theory" if its classifying topos is equivalent to the topos of presheaves on some small category.
The class of presheaf-type theories contains the class of algebraic theories but is much larger.
Theories of this class share general properties which are associated in our mind with algebra. They can be summarized by stating that presheaf-type theories are those whose semantics and syntax are equivalent.
We shall recall these properties which are mainly due to Olivia Caramello.
Then we shall present a criterion for verifying concretely that a theory is presheaf-type and we shall illustrate how it can be applied in particular instances.
