# 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.

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### How to say these two distinct functions have the same structure?

Yesterday, I posted this question, which remains unanswered. In this related question, I ask a different yet more precise question that may help me solve the other question. Let $N=\{1,2\}$ be a two-...
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### What are colored morphisms/arrows intended to mean in these diagrams?

I've been reading more category theory as a prerequisite to understanding some more complicated theorems, and for the first time I'm running into arrows that are distinctly colored. Examples include ...
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### Is Inverse of bijective morphism also morphism?

Let $V_1,V_2$ be affine varieties. Let $f$ be a morphism(https://en.wikipedia.org/wiki/Morphism_of_algebraic_varieties) between $V_1,V_2$. If $f$ is bijective, is inver of $f$ also morphism ? If not, ...
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Can someone please explain it to me what does the highlighted text mean? I am trying to learn Algebraic Geometry from Fulton and Shafarevich but I am stuck now. This says that to check whether an $m-$...