Questions tagged [fibered-products]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
13 votes
2 answers
290 views

Does a fibre product of a group $G$ with itself have a subgroup isomorphic to $G$?

Let $G$ be a group, and consider a fibre product of the form $H=G\times_{D,\phi,\psi}G$, i.e. the group of pairs $(g,g'),\phi(g)=\psi(g')$, for some surjective group morphisms $\phi:G\rightarrow D$ ...
Antoine's user avatar
  • 163
2 votes
0 answers
205 views

$2$-fiber products

Let $\cal{C}$ be a $2$-category. Then there is a notion of a $2$-fiber product (see ncatlab or Stacksproject). This notion is quite elaborate and lengthy to define. However, one can try to give a more ...
tautautua's user avatar
1 vote
0 answers
126 views

Which object related to families of algebraic varieties over a scheme $ S $ corresponds to the tensor product of vector bundles?

I asked yesterday on math.stackexchange.com that if the fiber product of two vector bundles seen in general as the fiber product of two families of special algebraic varieties over a scheme $ S $ ...
YoYo's user avatar
  • 325
1 vote
1 answer
321 views

Automorphism group of fiber products of schemes

Let $A \mapsto S$ and $B \mapsto S$ be two schemes over the scheme $S$. Is there a connection between the automorphism group of the scheme $A \otimes_{S} B$ and the automorphism groups of $A$ and $B$ ?...
THC's user avatar
  • 4,313
2 votes
0 answers
143 views

On subdirect products [closed]

I'm sorry if this question doesn't fit with MO rules, but I've asked on Math SE yet without answers, so I post here with the hope someone will answer me. I want to show, knowing the Goursat's theorem,...
HaroldF's user avatar
  • 433
7 votes
1 answer
697 views

Fiber vs homotopy fiber in model categories: simple question

I have a concrete problem with the homotopy fiber and I am getting lost with the literature. I state my question and, to avoid confusions, I state downwards the definitions I am using. Let $C$ be a ...
Tintin's user avatar
  • 2,721
11 votes
1 answer
2k views

Does pullback in the category of smooth manifolds always exists?

I am looking for an example where $f:Y\to X$ and $f':Y'\to X$, are both smooth maps of smooth manifolds, but the pullback does not exist. Remarks: 1) A pullback in a certain category is defined as ...
Asaf Shachar's user avatar
  • 6,611
2 votes
0 answers
227 views

Mayer-Vietoris on Fibered Products

Suppose $M \xrightarrow{p} X$ is a surjective submersion of smooth manifolds. Define the fibered product in this case: $$M \times_X M = \{ (m_1, m_2) \in M \times M | p(m_1) = p(m_2) \}$$ and let $U =...
cheyne's user avatar
  • 1,396
11 votes
2 answers
3k views

Is Sheafification Functor Exact?

I know that sheafification functor from the category of abelian presheaves on $C$ to the category of abelian sheaves on $C$. Here, $C$ is a category with Grothendieck pretopology. My question is: ...
Hiro's user avatar
  • 945
12 votes
3 answers
3k 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 ...
Hiro's user avatar
  • 945
1 vote
1 answer
1k views

Codimension of points in fibered products

This is a question about a proof in Hartshorne, but let me try to formulate it without reference to Hartshorne. Let $X$ be a noetherian scheme (which is also integral, separated and regular in ...
darij grinberg's user avatar