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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What is the link between homomorphisms and mutual information?

Intuitively, there seems to be a link between the (kind of) homomorphism between two algebraic structures and the mutual information between two variables. However, since I'm not a mathematician, it's ...
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49 views

Why are “the” morphisms of the category of topological spaces continuous maps?

On the Wikipedia page for "morphism (category theory)" it says that: In the category of topological spaces, morphisms are continuous functions and isomorphisms are called homeomorphisms. In what ...
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Extension of projection from a point to a Blow Up

I feel like there's something obvious I'm missing here, and I'm not looking for a whole answer, but rather just a pointer in the right direction. Suppose you have the projection from a point ...
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Functions which map Lebesgue measurable sets into Lebesgue measurable sets

Can you give an alternative description of the set of functions which map Lebesgue measurable sets into Lebesgue measurable sets? I think that it is enough to consider Lebesgue measurable sets on the ...
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Gröbner degeneration, flat families and morphism of varieties.

I am trying to understand why a map is actually a morphism of varieties. The map, from the affine line to the Hilbert scheme of points, is given by a Gröbner degeneration from an ideal I to its ...