# Questions tagged [morphism]

In category theory, a morphism is a structure-preserving map, such as continuous mappings on topological spaces, measurable functions, and linear maps.

251 questions
Filter by
Sorted by
Tagged with
29 views

38 views

118 views

### help with Kernel and image of an endomorphism

I am given the kernel and image of an endomorphism in $\Bbb R^3$, which are: $\ker f =\langle(1,1,0)\rangle$ $\text{Im}\, f = \langle(0, 1, -1), (2, 1, 2)\rangle$ and I have to find the matrix ...
295 views

### Does a would-be isomorphism between a known and suspected category object guarantee the latter object to be in the category?

In this question from a few day ago, it became evident that, given a known vector space $(V,+,\times)$, a possible vector space $(W,\oplus,\otimes)$, and a transformation $T:V\rightarrow W$ that is is ...
106 views

### diagonal morphism preserves properties that are satisfied by isomorphisms under base-change

Let $\mathcal{P}$ be a property of morphisms of schemes that is fulfilled by isomorphisms. Now assume we have a property $\mathcal{P}$ that is invariant under base-change, that means if $f:X \to Y$ ...
### Show that $\mathbb{R}^n$ is a direct sum of lines and planes
Let $A \in M_n(\mathbb{R})$ be a matrix which is diagonalizable in $M_n(\mathbb{C})$. We note $u_{A, \mathbb{R}}: \mathbb{R}^n \rightarrow \mathbb{R}^n$ the endomorphism defined by the left ...