This sort of ? is a relic of an old mistaken database edit that clobbered some unicode symbols, and should be fixed wherever they appear. Thanks!

]]>There were some ?s. The first I changed to infinity and the rest to alephs. The ?s are new to me, so I hope I didn’t misunderstand their purpose.

]]>fixed a small typo

]]>Replaced characters ’ř’ that had turned into ’?’ in links to the pages Jiří Adámek and Jiří Rosický

]]>Fixed. There were some spurious line breaks.

Also, I changed to section link to something more likely to be permanent.

]]>Is it just my browser? The table here doesn’t display properly for me.

]]>Sorry, could you point directly to what you are looking at? The table which I do see is not broken, but likely I am not looking at the table which you have in mind. Sorry.

]]>There’s a table in the ’summary and overview’ section which I don’t know how to fix.

]]>I have edited a bit more. I think now essentially all the material is there that should go there. But some more glue should still be added.

]]>I have edited a bit more at *locally presentable categories - introduction*. Mostly I tried to fill in data in the second and third main sections, but for the moment it remains skeletal.

I have to quit now. Will come back to this in a few hours. Would be happy about whatever comments or even edits you’d have meanwhile.

]]>Thanks. That’s a good point. Actually, the relation between “compact” as in “compact topological space” as well as “compact topos” on the one hand and in “compact object in a category” on the other is somewhat subtle. The thing is that the former two are really conditions to commute with filtered colimits of *truncated objects*/truncated morphisms.

I have once made some notes on this in section 3.3.3 here.

]]>Good idea! It might be worth explaining why we use *filtered* colimits rather than arbitrary ones. It seems to me that the idea is that if one has a compact object, then its image under any morphism should be “small” in the sense that any “cover” of it can be reduced to a finite one. So, if we enlarge the “covering system” so that it is closed under finite “unions”, then we get a filtered system, and the object is compact precisely when every morphism factors through a *single* object in the “covering system”, and this factorisation is unique modulo a certain equivalence relation which amounts to saying that homs out of a compact object preserve filtered colimits.

I was looking for a place to record a somewhat more global overview of the notion of *locally presentable category*, its related notions and its generalizations to higher category theory. But somehow all of the existing entries feel too narrow in focus to accomodate this. So I ended up creating now a new entry titled

Think of this as accomodating material such as one might present in a seminar talk that is meant to bring people with some basic background up to speed with the relevant notions, without going into the wealth of technical lemmas.

I only just started. Will continue in a moment after a short break…

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