We will continue on Thursday, October 10, in M5 at 1pm by the talk

J. Adamek

Finitary functors

Abstract:
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.