16 дек. 2017 г. · The presentable objects in the category of general topological spaces are the discrete ones (it's a very known joke). A topological space is λ- ...

24 нояб. 2020 г. · We say that A is compact (or sometimes small) if whenever we have a morphism u:A⟶⨁i∈IAi from A into a nonempty coproduct, there is a nonempty ...

23 сент. 2024 г. · 1 Answer 1 ... Idem is in fact compact - it is a retract of the following finite category C: it has a single object x, and is free on an the ...

8 апр. 2024 г. · I am interested in the compact objects of various categories of categories. For example, Catsmall is presentable and has compact objects ...

1 июн. 2021 г. · A category is C is strongly compact if and only if every COCONTINUOUS functor satisfies the solution set condition. This makes things different.

3 дек. 2014 г. · Small objects vs Compact objects ... Given a cocomplete category C, is there an example of an object which is small but not compact? I am working ...

25 мая 2020 г. · Yes, it is. The reason is: every object of your presheaf category is a colimit of representables;; so, every object is a filtered colimit of ...

20 окт. 2012 г. · I guess that in an infinity category, one also defines a compact object as an object, Hom from which commutes with homotopy filtered colimits.

24 янв. 2024 г. · In a locally presentable category, is every object (a retract of) the colimit of a chain of smaller objects?

25 апр. 2012 г. · In an (∞,1)-category C, one says that an object X is κ-compact if the representable functor Hom(X,−):C→∞Gpd preserves κ-filtered (∞,1)- ...