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Reed Mullanix (Jan 31 2021 at 21:15):So I've been reading through "Locally Presentable and Accessible Categories", and I can't seem to figure out how exactly you go from preserving filtered colimits to being able to factor morphisms out of into some filtered colimit through one of the colimit inclusions.
More concretely, I know that we need to use the fact that is a colimit in , I just can't figure out what cocone we should build to map into.
Reid Barton (Feb 01 2021 at 01:17):Don't try to map it into anything; instead use the fact that in Set, every element of the colimit is the image of some element of some object in the diagram.
Reid Barton (Feb 01 2021 at 01:19):(You could prove this by mapping the cocone into {false, true}, but you can also just see it by the way you construct colimits in Set, as a quotient of a disjoint union.)
Reed Mullanix (Feb 01 2021 at 03:13):Ah, that would explain why I kept running into brick walls, thanks :smile: