Quantum Functor $Mor$

Abstract

Let $To{p}_c$ be the category of compact spaces and continuous maps and $To{p}_f\subset To{p}_c$ be the full subcategory of finite spaces. Consider the covariant functor $Mor:To{p}_f^{op}\times To{p}_c\to To{p}_c$ that associates any pair $(X,Y)$ with the space of all morphisms from $X$ to $Y$. In this paper, we describe a non commutative version of $Mor$. More pricelessly, we define a functor $\mathfrak{Mor}$, that takes any pair $(B,C)$ of a finitely generated unital C*-algebra $B$ and a finite dimensional C*-algebra $C$ to the quantum family of all morphism from $B$ to $C$.

11 pages, The last section of the paper completely changed

References in corpus (1)

• Quantum families of maps and quantum semigroups on finite quantum spaces

Cited by in corpus (3)

• A Kind of Compact Quantum Semigroups
• On the structure of noncommutative mapping schemes
• Quantum metric spaces of quantum maps