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The problem is that the question is highly dependent on the definition of $n$-groupoids. The notion of strict $n$-groupoid is very clear and precise but we know very well (and Grothendieck knew that) …

This follows from two Facts: 1) A category monadic over Set/S is always an exact category. That is it has quotient by equivalence relation that are effective and universal. It is in particular a regu …

As the title said, I would like to know if constructive measure theory has been developed somewhere ? I am more precisely interested in the (constructive) theory of completely continuous valuation on …

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 …

The following theorem is relatively classical: Theorem: Given an accessible endofunctor, (co)pointed endofunctor or (co)monad $T$ on a locally presentable category $C$, then the category of $T$-(co)a …

I'm looking for references presenting a constructive treatment of the theory of ordinals. By constructive I mean valid in the internal logic of a topos (so no axiom of choice and no law of excluded mi …

This notion of convergence is not often refered to; I think mostly because it does not come from a topology. But this an excellent notion of convergence, probably the best we can put on the space of ( …

This has been called a "fc-multicategory" by Tom Leinster, for example here. I think this as also been called a "Hypervirtual double category" here, but I don't remember if this is exactly the same …

As I said in the comment, this would involve a very large number of different references! (almost one by subsection...) But to some extent, contributors to the nLab already started doing that and it i …

For this type of question the first reference that comes to my mind is P.T.Johnstone Sketches of an elephant, part C. Most of the results in this book are constructively valid: If a result is proved …

Is there any references on the tensor product of (locally) presentable categories ? All I know about this is Lurie's book that deals with the $\infty$-categorical version, and a few references that d …

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 …

If you are willing to accept internal argument instead of purely categorical (external) one, a very good reference for this is Palmgren and Vickers' paper: " Partial Horn Logic and cartesian categorie …

Is there a known description of the free category with both product and coproduct? That is, given a small category $C$, I want to consider a category $U C$ which has product and coproduct, a functor $ …

In Higher topos theory and Higher algebra Lurie defines (see section 2.3.1 of HTT) a correspondence between two $\infty$-categories $C$ and $D$ as being an $\infty$-category $\mathcal{M}$ over $\Delta …