Algebraic functor slices
\textit{J. Sichler} and \textit{V. Trnková} introduced the notion of functor slice in their paper ``Functor slices and simultaneous representations'' [Contrib. Gen. Algebra 7, 299-320 (1991; Zbl 0742.18005)]. That notion leads to an equivalence relation for functors, called slice-equivalence or \(s\)-equivalence. In particular, concrete categories with standard forgetful functors are said to be \(s\)-equivalent whenever their forgetful functors are \(s\)-equivalent. There are several baskets of concrete categories whose members are mutually \(s\)-equivalent. The purpose of the paper is to enrich the one which contains the category \(\text{Alg}(\Delta^ +)\) of all universal algebras of positive type \(\Delta^ +\) and their homomorphisms. Two theorems are given which allow to recognize that the following concrete categories belong to the above basket: (a) The category \(\text{Ban}_ 1\) of Banach spaces and contracting linear maps with the unit-ball functor taken as forgetful functor \(U:\text{Ban}_ 1\to\text{Set}\). (b) The category Comp of compact Hausdorff spaces and continuous maps together with all its full subcategories down to the category of extremely disconnected spaces.
scientific article; zbMATH DE number 89553
scientific article