# Tagged Questions

**2**

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**0**answers

353 views

### The link between the subfactors and the motives as enriched Galois theories?

On 29th March 2007, at the "École normale supérieure" of Paris, the mathematician Vaughan Jones, gave a conference (in French) entitled "Les sous-facteurs : une théorie de Galois enrichie" (see here), ...

**5**

votes

**1**answer

353 views

### Noncommutative geometry and category theory

The point in which one starts to talk about noncommutative geometry is the Gelfand Najmark theorem. It establishes an equivalence of the catgeories of commutative (non)unital $C^*$-algebras and the ...

**1**

vote

**0**answers

180 views

### Fusion categories with permutation “associativity matrices”

Let $\mathcal{C}$ be a fusion category and let $(H_1,...,H_r)$ be its simple objects.
$\mathcal{C}$ is non-pointed if at least one of its simple object has Perron-Frobenius dimension $ \neq 1$.
...

**2**

votes

**1**answer

176 views

### Functors with an epi-mono factorization property

This is a simple question about terminology and a request for any related references. Specifically, what would you call a functor $F:\mathbf{D}\rightarrow\mathbf{C}$ with the following property?
...

**7**

votes

**1**answer

295 views

### Defining holomorphic functions in terms of Banach algebras, and similarly for C*-algebras

Let $C$ be the category of commutative Banach algebras and let $U : C \to \text{Set}$ be the usual forgetful functor. The holomorphic functional calculus guarantees that every holomorphic function $f ...

**6**

votes

**1**answer

281 views

### Tannaka duality for C*-algebras?

Tannaka-Krein
duality shows
how to recover a group $G$ from its category $\mathbf{Rep}(G)$ of finite-dimensional
complex representations and the forgetful functor $F:\mathbf{Rep}(G)\to
...

**15**

votes

**1**answer

786 views

### Convolution algebras for double groupoids?

There is a lot of work of course on convolution algebras of measured groupoids, and this gives "Noncommutative geometry". However there is a lot of interest in algebraically structured groupoids, for ...

**9**

votes

**1**answer

452 views

### Mono- and epi-morphisms for C*-algebras

This question is motivated by Yemon Choi's answer here: Epimorphisms have dense range in TopHausGrp?
It's well-known that the category of unital commutative C*-algebras and $*$-homomorphisms is dual ...

**5**

votes

**1**answer

249 views

### Does there exist any massive proper $C^*$-subalgebra?

Definition 1: Suppose $B$ is a $C^* $-algebra. $A$ is massive $C^* $-subalgebra of $B$ iff
1. $A$ is a subalgebra of $B$;
2. for each irreducible representation $\pi$ of $B$ representation $\pi|_A$ is ...

**0**

votes

**2**answers

790 views

### Quantum channels, question 2: tensor products and composition of functions

Please be kind. I've been working on this for a long time and can't find an answer. Feel free to edit for clarity if you think the question can be better worded.
Background
It may help to see a ...

**1**

vote

**0**answers

587 views

### Tensor products as isomorphic functors in category theory

An earlier question that I posed sought to define a category with a set of quantum channels as arrows and the C$^{*}$-algebra that these channels map from and to as the object. So, for example, my ...

**5**

votes

**4**answers

601 views

### Quantum channels as categories: question 1.

A quantum channel is a mapping between Hilbert spaces, $\Phi : L(\mathcal{H}_{A}) \to L(\mathcal{H}_{B})$, where $L(\mathcal{H}_{i})$ is the family of operators on $\mathcal{H}_{i}$. In general, we ...