All Questions
Tagged with hilbert-spaces ct.category-theory
8 questions
4
votes
0
answers
169
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Drinfeld center of a tensor category
Firstly, apologies for the imprecise language, I'm a physicist trying to understand anyonic excitations from the lens of category theory.
If I have a category (say $\operatorname{Rep}(\mathbb{Z}_2)$) ...
- 569
0
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0
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197
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Link between a categorical and an algebraic characterization of (infinite-dimensional) Hilbert space
On one side, a very recent paper of Chris Heunen and Andre Kornell "Axioms for the category of Hilbert spaces" (Arxiv:2109.7418v1 latest Arxiv version) offers a characterization of the ...
- 2,655
64
votes
6
answers
10k
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Are dagger categories truly evil?
Recall that a dagger category is a category equipped with an involution $*:Hom(x,y)\to Hom(y,x)$ that satisfies $f^{**}=f$ and $f^* g^*=(gf)^*$. A prominent example of a dagger category is the ...
- 43.2k
1
vote
1
answer
136
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Is $\textbf{FHILB}$ locally regular?
Is the category, $\textbf{FHILB}$, of finite dimensional Hilbert spaces and linear maps locally regular, where `locally regular' is defined like this
http://ncatlab.org/nlab/show/locally+regular+...
- 631
20
votes
0
answers
2k
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Can the similarity between the Riesz representation theorem and the Yoneda embedding lemma be given a formal undergirding?
For example, by viewing Hilbert spaces as enriched categories in some fashion? (I suppose the same idea of considering the inner product of a Hilbert space as a generalized Hom-set has also been ...
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19
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1k
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Is there some way to see a Hilbert space as a C-enriched category?
The inner product of vectors in a Hilbert space has many properties in common with a hom functor. I know that one can make a projectivized Hilbert space into a metric space with the Fubini-Study ...
- 1,532
3
votes
1
answer
2k
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Does the category of Hilbert spaces possess a product?
I've been studying some category theory lately and in particular, I became acquainted with the notions of products and coproducts, which led me to ponder the following:
Consider the category of all ...
- 4,874
15
votes
2
answers
2k
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What is a projective space?
Is there a "recognition principle" for projective spaces?
What categories are there with projective spaces for objects?
Background: Although the title is a nod to What is a metric space?, ...
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