Paper Info
Title
On Equalizers In The Category Of Locales
Abstract
The fact that equalizers in the context of strongly Hausdorff locales (similarly like those in classical spaces) are closed is a special case of a standard categorical fact connecting diagonals with general equalizers. In this paper we analyze this and related phenomena in the category of locales. Here the mechanism of pullbacks connecting equalizers is based on natural preimages that preserve a number of properties (closedness, openness, fittedness, complementedness, etc.). Also, we have a new simple and transparent formula for equalizers in this category providing very easy proofs for some facts (including the general behavior of diagonals). In particular we discuss some aspects of the closed case (strong Hausdorff property), and the open and clopen one.
Year
DOI
Venue
2021
10.1007/s10485-020-09616-8
APPLIED CATEGORICAL STRUCTURES
Keywords
DocType
Volume
Frame, Locale, Sublocale, Localic map, Image and preimage, Binary product of locales, Strongly Hausdorff locale, Diagonal map, Equalizer, Open diagonal
Journal
29
Issue
ISSN
Citations 
2
0927-2852
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Jorge Picado12010.18
Ales Pultr27224.12