Categories of Boolean sheaves of simple algebras
type: Item
instance of: scholarly article
title: Categories of Boolean sheaves of simple algebras
zbMATH Open document ID: 0594.18007
author: Yves Diers
published in: Lecture Notes in Mathematics
publication date: 1986-01-01T00:00:00Z
review text: This book takes the axiomatic point of view toward sheaf representation theorems. There are three chapters: Categories of Boolean sheaves of algebras; Categories of Boolean sheaves of simple algebras (including various Galois theories); and Categories of locally Boolean sheaves of simple algebras. Details of the development must be left to the work itself, but here is a bit of the flavor. A category is locally indecomposable if it is locally finitely presentable, the product of the initial object with itself is finitely presentable, and the finite products are codisjoint and couniversal. A direct factor of an object \(A\) is a quotient \(f: A\to B\) for which there exists \(g: A\to C\) so that \((f,g)\) makes \(A\) a product of \(B\) and \(C\). An object is indecomposable if it has exactly two direct factors. Theorem 1.7.3: Any locally indecomposable category is equivalent to the category of sheaves of indecomposable objects on Boolean spaces. Those readers interested in such results will want to compare and contrast the paper by \textit{M. Coste} [Applications of sheaves, Proc. Res. Symp., Durham 1977, Lect. Notes Math. 753, 212--238 (1979; Zbl 0422.18007)].
reviewed by: Don H. Van Osdol
Mathematics Subject Classification ID: 18C10
Mathematics Subject Classification ID: 18-02
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 06E99
Mathematics Subject Classification ID: 18B30
Mathematics Subject Classification ID: 18D99
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 3955180
zbMATH Keywords: locally finite presentable category
zbMATH Keywords: locally indecomposable
zbMATH Keywords: category
zbMATH Keywords: sheaf representation
zbMATH Keywords: sheaves of algebras
zbMATH Keywords: Boolean sheaves of simple algebras
zbMATH Keywords: Galois theories
zbMATH Keywords: locally Boolean sheaves
zbMATH Keywords: direct factor
zbMATH Keywords: indecomposable objects
zbMATH Keywords: Boolean spaces
MaRDI profile type: Publication
DOI: 10.1007/BFB0075887
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description: scientific article; zbMATH DE number 3955180