Questions tagged [fibered-products]
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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 $\phi:G\rightarrow D$ ...
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$2$-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 ...
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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 $ ...
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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 $B$ ?...
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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,...
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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 ...
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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 ...
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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 =...
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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:
...
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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 ...
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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 ...