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.
