**2**

votes

**0**answers

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

**0**answers

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

**2**answers

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

**3**answers

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

**1**answer

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

**2**answers

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

**1**answer

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 ...