Sadr, Maysam Maysami Quantum functor \({\mathcal M}or\). (English) Zbl 1240.46079 Math. Pannonica 21, No. 1, 77-88 (2010). Summary: Let \({\mathcal T}op_c\) be the category of compact spaces and continuous maps and \({\mathcal T}op_f\subset {\mathcal T}op_c\) be the full subcategory of finite spaces. Consider the covariant functor \({\mathcal M}or:{\mathcal T}op^{op}_f\times {\mathcal T}op_c\to {\mathcal T}op_c\) 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 \({\mathcal M}or\). More precisely, we define a functor \(\mathfrak M\mathfrak o\mathfrak r\) 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 \(C\). As an application, we introduce a non-commutative version of the path functor. Cited in 1 Document MSC: 46L05 General theory of \(C^*\)-algebras 46L85 Noncommutative topology 46M15 Categories, functors in functional analysis Keywords:category of \(C^{\ast}\)-algebras; quantum family of maps; non-commutative algebraic topology PDFBibTeX XMLCite \textit{M. M. Sadr}, Math. Pannonica 21, No. 1, 77--88 (2010; Zbl 1240.46079) Full Text: arXiv