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Results tagged with ct.category-theory
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user 61785
Enriched categories, topoi, abelian categories, monoidal categories, homological algebra.
2
votes
Real/complex addition, multiplication, and exponentiation from a categorical viewpoint?
In category theory exponentiation is not a natural transformation. Rather, it is a functor, or a family of functors, equipped with a natural transformation.
If we have a category $C$ with finite pro …
- 3,768
6
votes
Exponential objects in the category of measurable spaces
It is also possible to show that the category of measurable spaces, $\newcommand{\Mble}{\mathbf{Mble}}\Mble$, is not cartesian closed by using more category theory and less measure theory (though stil …
- 3,768
1
vote
Accepted
Functor from rings into compact Hausdorff spaces
Here is an answer to your question about monadicity, as it's too long for a comment. I will not fill in every detail, so if you follow along there will be several definitions that need to be expanded …
- 3,768
11
votes
Who needs Replacement anyway?
Here's an example of a published, nontrivial use of the the product of the sequence $\{ V, V^{*}, V^{**}, \ldots \}$ in a functional analysis paper, for the specific case of $V = \mathbb{R}^{\mathbb{N …
- 3,768