Epimorphisms and maximal covers in categories of compact spaces

B. Banaschewski; A. W. Hager

doi:10.4995/agt.2013.1616

Authors

B. Banaschewski McMaster University
A. W. Hager Wesleyan University

DOI:

https://doi.org/10.4995/agt.2013.1616

Keywords:

Epimorphism, Cover, Projective, Essential extension, Compact, Strongly rigid

Abstract

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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Author Biographies

B. Banaschewski, McMaster University

Department of Mathematics and Statistics

A. W. Hager, Wesleyan University

Department of Mathematics and Computer Science

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