Algebraic functor slices
type: Item
instance of: scholarly article
title: Algebraic functor slices
zbMATH Open document ID: 0760.18003
DOI: 10.1016/0022-4049(92)90110-2
author: Věra Trnková
author: Václav Koubek
author: Jiří Sichler
published in: Journal of Pure and Applied Algebra
publication date: 1993-01-16T00:00:00Z
review text: \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.
Mathematics Subject Classification ID: 18A22
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 18B30
zbMATH DE Number: 89553
zbMATH Keywords: slice-equivalent functors
zbMATH Keywords: \(s\)-equivalent
zbMATH Keywords: concrete categories
zbMATH Keywords: functor slice
zbMATH Keywords: universal algebras
zbMATH Keywords: Banach spaces
zbMATH Keywords: compact Hausdorff spaces
reviewed by: Heinrich Kleisli
MaRDI profile type: Publication
full work available at URL: 0022-4049(92)90110-2
OpenAlex ID: W1997533152
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description: scientific article; zbMATH DE number 89553