Search Results

I asked this on math.stackexchange.com, but didn't get any answer. Let $\mathcal{A}$ be an abelian category and $\mathcal{C}$ a localizing subcategory in the sense of Gabriel. (A Serre/thick/dense su …

If everything takes place in the category of compactly generated spaces, it holds $$\pi_0(BC)=\pi_0(obC)/\tilde{},$$ where two path components in the object space get identified, if there are objects …

Almost all of your questions are answered in Pierre Gabriel's dissertation "Des catégories abéliennes". He shows in a more general case, that the left exact functors between nice abelian categories a …

Let $C$ be a small category and $F\colon C^{op}\rightarrow Set$ a functor. The Grothendieck construction is the category $F\wr C$ with objects being pairs $(c,x)$ where $c$ is a object of $C$ and $x\i …

The Freyd-Mitchell embedding theorem states the following: Let $\mathcal{A}$ be a small abelian category. There exists a unital ring $R$ and a full, faithful and exact functor $F\colon\mathcal{A}\ …

Here's a direct way of seeing it, without using the Quillen equivalence to simplicial sets equipped with the Joyal model structure: The cofibrant objects in the Bergner model structure are the 'simpl …

This is a follow-up to Dan Ramras' answer of this question. The following correction can be found in the errata to The Geometry of Iterated Loop space (Page 484 here). The weak Hausdorff rather t …