# Tagged Questions

**8**

votes

**2**answers

334 views

### Is the category of schemes wellpowered? regularly wellpowered?

Wellpowered means that for every scheme $X$, the subobject lattice of monormophisms $Y \to X$ is essentially small; regularly wellpowered means that for every scheme $X$, the regular subobject lattice ...

**5**

votes

**0**answers

65 views

### Category of the smooth formal p-groups over a local ring

Fontaine showed in Asterisque 47-48 that the category of finite dimensional smooth formal $p$-groups over the ring $A=W(k)$ of the Witt vectors over a finite field $k$ is anti-equivalent to the ...

**3**

votes

**2**answers

332 views

### K-Theory of Schemes: Monoidal vs. Exact

There are several ways for defining the K-Theory of a category depending on which structure it admits. The K-Theory of schemes is commonly defined as the "group completion" of the category of ...

**6**

votes

**3**answers

738 views

### Do Disjoint Unions and Fiber Products Commute?

Do disjoint unions and fiber products commute?
In other words, is the following statement true?
Statement: Let $C$ be a category with (infinite) coproducts and fiber products. Let {$U_{i}$} be a ...

**15**

votes

**1**answer

1k views

### What are the epimorphisms in the category of schemes?

Is there a known characterization of epimorphisms in the category of schemes?
It is easy to see that a morphism $f : X \to Y$ such that the underlying map $|f|$ is surjective and the homomorphism ...

**2**

votes

**2**answers

424 views

### Do affine schemes form a Mal'cev category?

This may be a silly question, but I have no intuition in this direction. Every category internal to a Mal'cev category is a groupoid (this is why categories internal to $Grp$ are groupoids). If this ...

**17**

votes

**6**answers

1k views

### Categorical construction of the category of schemes?

The answer to the following question is probably well known or the question itself is well known not to have a reasonable answer. In the latter case could you please let me know what the "right" ...

**10**

votes

**1**answer

675 views

### Construction of the petit Zariski topos out of the gros topos of a scheme

Let S be a scheme. Let (Sch/S) be a small category of schemes over S (including essentially all finitely presented schemes affine over S). Let E = (Sch/S)zar denote the gros Zariski topos with its ...

**3**

votes

**3**answers

555 views

### Affine morphisms in different settings coincide?

1.If we identify two schemes $X$ and $Y$ as two presheaves of set on category of affine schemes.($Aff:=\text{CRing}^{op}$) If there is a morphism as natural transformations $f:X\to Y$, then, how to ...