Seminář se koná 9.10.2019 od 16:30 v Mendelově muzeu.

Dana Stewart Scott

Enumeration Operators, Probability, Type Theory

Abstract:

For a long time it has been known that enumeration operators on the powerset of the integers form a model of the λ-calculus. More recently, the speaker realized that well-known methods allow for the adjunction of random variables to the model. Also other well-known ideas can expend the basic model into a model for Martin-Löf type theory. Some recent work with a group of collaborators combines the two approaches by invoking Boolean-valued models. The talk will address the question of how to give this natural modeling interesting applications.

Další seminář z algebry se koná 10.10.2019 od 13.00 v posluchárně M5.

J. Adamek

Finitary functors

Abstrakt:
Every finitary functor F between locally finitely presentable categories is finitely bounded, i.e., finitely generated subobjects of each FX factorize through the image (under F) of finitely generated subobjects of X. Conversely, finitely bounded functors preserving monomorphisms are finitary.
We discuss conditions under which 'finitary = finitely bounded' holds for a l l functors. This is true e.g. for atomic Grothedieck toposes with finitely many finitely presentable atoms.
We also study the finitely presentable objects in the categories [Set,Set]_fin of all finitary set functors and Mnd_fin(Set) of all finitary monads over Set.