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If it is not in bourbaki, I don't have a reference in mind, but here is a proof : Let $(B_n)$ for $n \in \mathbb{N}$ be any countable family of entourage. Then because each $B_n$ is an entourage one …

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 don't think this has been considered. Mainly I've never seen it, but also there are specific feature of this notions that makes it unlikely to be a relevant category theoretic notion independently o …

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 …

One can find in the literature two notions of $C^*$-algebra over a topological space $X$. The first is as the data of an open surjection $ \pi: B \rightarrow X$ together with the structure of a $C^*$ …

There are essentially two ways to impose extentionality on a type theory (I know, it is not very fashionable to impose extentionality these days, but please, bear with me) you can either have a "propo …

I am looking for a reference for the following result: If $A$ and $B$ are C* algebras, $H$ is a right Hilbert $A$-modules, $\phi :A \rightarrow B$ is a morphism, and assume that there is a map $\eta …

Unless I'm mistaken the "Free completion under finite limits monad" $C \mapsto C^{lex}$ and the "free co-completion monad" $C \mapsto \widehat{C}$ (the categories of small presheaves) satisfies a dist …

I think the question is vague and probably does not have a unique answer. I would says that this kind of concern is actually not so different from the "size issue " generally presented by the set of …

If $G$ is, for example, a finite directed graph, one can attach to it a topos $T_G$ whose objects are "$G$-sheaves". A $G$-sheave $F$ is the data of: For each verticies $x$ a set $F(x)$, for each arr …

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 …

(note: this question is essentially a reference request for the tensor product described at the end. the rest is context) It is well known that the category of chain complexes (in positive degree, wi …

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 …

Given $C$ a small category (eventually, a small simplicial category) I denote by $UC$ the projective model structure on the category of simplicial presheaves on $C$ as in the paper. Using the kind of …

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 …