Arguments working entirely at a high level of abstraction, particularly category-theoretic arguments.

learn more… | top users | synonyms

2
votes
0answers
203 views

Why does this setting imply that a category is Grothendieck?

I came across the following Lemma in Mitsuyasu Hashimoto's Equivariant Twisted Inverses; it is Lemma 11.2 on page 107 of this pdf. Let $\mathcal{A}$ be an abelian category which satisfies the (AB3) ...
0
votes
0answers
99 views

Finite separable extension of fields imply the number of intermediate subfield is finite

The proof of statements either uses Galois theory or Artin primitive element theorem.I would like to know whether there is a proof without using these.The reason to avoid using Galois theory is that ...
5
votes
2answers
208 views

Is there a measure / probability theory in a topos of “generalized measure spaces”?

Consider the category with the standard Lebesgue measure space $\Omega$ as its only object and measure type preserving nonincreasing (equivalence classes of) maps as morphisms. Question: is there an ...
4
votes
3answers
756 views

The ABC of categories: ABstract vs Concrete

From Wikipedia: A concrete category is a category that is equipped with a faithful functor to the category of sets. This functor makes it possible to think of the objects of the category ...
4
votes
1answer
280 views

Are strict pushout squares in Cat exact squares?

Let $C,C',D\in \operatorname{Cat}$, and consider the following strict pushout square $$\begin{matrix} C&\overset{f}{\to} &D^{op}\\ \downarrow^\pi&\swarrow&\downarrow^{\iota_2}\\ ...
2
votes
2answers
271 views

The single-plus construction is not the left adjoint of the inclusion of separated presheaves?

Convention: Before I start, please note that it is not going to be sufficient to assume that the topology is subcanonical or that the site $C$ has finite limits, since the application I have in mind ...
2
votes
1answer
450 views

Abstract classes of anodyne maps (relative to an interval) in a presheaf category are stable under smash products with monomorphisms?

Let $A$ be a small category, and let $X:=Psh(A)$ denote the category of presheaves on $A$. It is a theorem that for any such category $X$, there exists a small set $M$ of monomorphisms admitting the ...