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This is true. It is for example easy to see that the full subcategory of objects of this form is closed under all finite colimits*, dense and that these objects are all finitely presentable. I unfortu …

I'm not aware of litterature on this, but this is something I have thought about several years ago and never ended-up using or publishing. What is below is me trying to remind myself how it works - un …

I'm looking for a reference that covers things like the lemma below - it doesn't have to be the exact statement I'm going to give, anything in the general ballpark would probably be useful. Or if you …

Is there an argument in the litterature that show that every locally presentable $\infty$-category is equivalent to the localization of proper combinatorial Quillen model category ? Of course if one r …

The answer to $1$ and $2$ are both yes. I don't know if this appears in the literature. The argument you give seems reasonable - I don't completely follow your notation but the general idea is that in …

These question of existence of free monad are not "derailling" the discusion. They are the whole point of the discusion. Let me clarify : If I'm not mistaken, we have the following: Theorem: Let $V$ b …

I just thought (or maybe remember) a neat proof of this fact. It involve ideas I worked on a few years ago but never published - but that's short enough so that I can explain the key ideas on MO. Let …

When you think about it the right way the idea is fairly simple : Here the "Free topos" means the "object classifier", that is the classifying topos of the theory with just one sort (one type) and no …

So the short answer is that there is no non-empty projective locales for essentially any reasonable class of epimorphisms you can think of (except maybe proper maps). The problem is that there exists …

I fix $C$ a symmetric monoidal model category (with a cofibrant unit if it helps). I'm assuming that it is closed, or at least that the tensor product commutes to colimits in each variable. If $X$ is …

For filtered diagram (as asked in the question) the answer is yes. Of course this fails for general diagram as mentioned in Harry's answer. Of course the "equivalence" has to be implemented by a pseud …

I know from the the theory of Artin groups that, as the $K(\pi,1)$ conjecture is known for Braids group, that using Salvetti complexes we have a fairly explicit finite CW-complex presentation of the c …

I'm looking for references for the following closely related facts: Given a Boolean algebra $B$, I denote by $\mathbb{Z}[B]$ the free ring generated by symbols $e_b$ such that $e_b e_{b'} = e_{b \cap …

I don't think the question as you asked with the construction you are describing as been explicitely treated in the literature (though it very well could be). What has been discused a lot in the litte …

If a category $C$ has limits of a certain type, then the category of monads on $C$ has the same type of limits, and these limits are computed "levelwise" (i.e. are preserved by the forgetful functor f …