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ArticleOriginal scientific text

Title

Bimorphisms in pro-homotopy and proper homotopy

Authors 1, 2

Affiliations

  1. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, U.S.A.
  2. Departamento Geometría y Topología, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain

Abstract

A morphism of a category which is simultaneously an epimorphism and a monomorphism is called a bimorphism. The category is balanced if every bimorphism is an isomorphism. In the paper properties of bimorphisms of several categories are discussed (pro-homotopy, shape, proper homotopy) and the question of those categories being balanced is raised. Our most interesting result is that a bimorphism f:X → Y of →w(H0) is an isomorphism if Y is movable. Recall that →w(H0) is the full subcategory of pro-H0 consisting of inverse sequences in H0, the homotopy category of pointed connected CW complexes.

Keywords

ENG
epimorphism, monomorphism, pro-homotopy, shape, proper homotopy

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Fundamenta Mathematicae
1999/160/3
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Pages:
269-286
Main language of publication
English
Received
1998-09-29
Accepted
1999-01-18
Published
1999
Exact and natural sciences