For question about morphism between groups, ring, topological spaces, vector space, categories, etcs... Please also use the correspondent tags (e.g. (group-theory), (ring-theory)) in order to precise the involved structure.
1
vote
1answer
52 views
Do nonsingular points get mapped to nonsingular points in a branched cover
Let $\pi:C\to D$ be a finite surjective morphism of noetherian integral schemes. Let $x\in C$ be a nonsingular point. Does it follow that $\pi(x)$ is nonsingular?
What if we impose some conditions ...
3
votes
3answers
342 views
Examples of categories where epimorphism does not have a right inverse, not surjective
Epimorphism is defined as following:
$f \in \operatorname{Hom}_C(A,B)$ is epimorphism if $\forall Z. \forall h', h'' \in \operatorname{Hom}_C(B, Z)$ the following holds: $h' f = ...
3
votes
1answer
211 views
the image of $1$ by a homomorphism between unitary rings
let $R$ and $S$ be unitary rings and $\phi:R\rightarrow S$ a ring homomorphism.
is the following correct:
$\phi(1_R\cdot1_R)=\phi(1_R)\cdot\phi(1_R)$ so $\phi(1_R)(1_S-\phi(1_R))=0_S$ and so ...
2
votes
0answers
183 views
Isomorphic measure-preserving systems: circle and torus
According to Definition 2.7 in
Ergodic Theory: with a view towards Number Theory,
the systems $(X, \mathcal{B}_X, \mu, T)$ and $(Y, \mathcal{B}_Y, \nu, S)$
are isomorphic when there is a $X' \in ...
2
votes
0answers
40 views
Can we embed K(X_eta) canonically in K(X)
Let $f:X\longrightarrow S$ be a morphism of schemes. Assume $X$ and $S$ are integral.
Let $\eta$ be the generic point of $S$ and let $X_\eta\longrightarrow \textrm{Spec} \ K(S)$ be the induced ...
2
votes
0answers
92 views
List of large classes of functors providing morphisms
I recently posted this question on mathoverflow and it was closed as being too localized. I am hoping to more precisely say what I mean here.
I recently learned, through my Topology coursework, that ...
5
votes
2answers
310 views
Morphisms in the category of natural transformations?
I am learning the basics of category theory, so this question is probably obvious to anyone who knows the subject.
The resources I've seen all take the following approach:
0) A category is a ...
2
votes
1answer
95 views
What are the most special spaces between which rigid transformations preserve the structures of the spaces
An affine transformation is a linear transformation followed by a translation. They are morphism between affine spaces.
A rigid transformation consists of a rotation and a translation. I was ...
