Epimorphisms and maximal covers in categories of compact spaces

• Banaschewski, B. ^[1] ; Hager, A.W. ^[2]
  1. [1] McMaster University

     McMaster University

     Canadá

     
  2. [2] Wesleyan University

     Wesleyan University

     Town of Middletown, Estados Unidos

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 14, Nº. 1, 2013, págs. 41-52
• Idioma: inglés
• DOI: 10.4995/agt.2013.1616
• Enlaces
  • Texto completo
• Resumen

  • 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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