Open AccessEpimorphisms and maximal covers in categories of compact spaces
Author(s) -
Bernhard Banaschewski,
Anthony W. Hager
Publication year - 2013
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2013.1616
Subject(s) - mathematics , subcategory , hausdorff space , cover (algebra) , projective test , class (philosophy) , projective cover , property (philosophy) , object (grammar) , pure mathematics , discrete mathematics , combinatorics , collineation , projective space , computer science , mechanical engineering , philosophy , epistemology , artificial intelligence , engineering
The category C is "projective complete"if each object has a projective cover (which is then a maximal cover). This property inherits from C to an epireflective full subcategory R provided the epimorphisms in R are also epi in C. When this condition fails, there still may be some maximal covers in R. The main point of this paper is illustration of this in compact Hausdorff spaces with a class of examples, each providing quite strange epimorphisms and maximal covers. These examples are then dualized to a category of algebras providing likewise strange monics and maximal essential extensions
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