Bimorphisms in pro-homotopy and proper homotopy

Jerzy Dydak; Francisco Ruiz del Portal

Fundamenta Mathematicae (1999)

  • Volume: 160, Issue: 3, page 269-286
  • ISSN: 0016-2736

Abstract

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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 t o w ( H 0 ) is an isomorphism if Y is movable. Recall that ( H 0 ) is the full subcategory of p r o - H 0 consisting of inverse sequences in H 0 , the homotopy category of pointed connected CW complexes.

How to cite

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Dydak, Jerzy, and Ruiz del Portal, Francisco. "Bimorphisms in pro-homotopy and proper homotopy." Fundamenta Mathematicae 160.3 (1999): 269-286. <http://eudml.org/doc/212393>.

@article{Dydak1999,
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 $tow(H_0)$ is an isomorphism if Y is movable. Recall that $(H_0)$ is the full subcategory of $pro-H_0$ consisting of inverse sequences in $H_0$, the homotopy category of pointed connected CW complexes.},
author = {Dydak, Jerzy, Ruiz del Portal, Francisco},
journal = {Fundamenta Mathematicae},
keywords = {epimorphism; monomorphism; pro-homotopy; shape; proper homotopy; pro-category},
language = {eng},
number = {3},
pages = {269-286},
title = {Bimorphisms in pro-homotopy and proper homotopy},
url = {http://eudml.org/doc/212393},
volume = {160},
year = {1999},
}

TY - JOUR
AU - Dydak, Jerzy
AU - Ruiz del Portal, Francisco
TI - Bimorphisms in pro-homotopy and proper homotopy
JO - Fundamenta Mathematicae
PY - 1999
VL - 160
IS - 3
SP - 269
EP - 286
AB - 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 $tow(H_0)$ is an isomorphism if Y is movable. Recall that $(H_0)$ is the full subcategory of $pro-H_0$ consisting of inverse sequences in $H_0$, the homotopy category of pointed connected CW complexes.
LA - eng
KW - epimorphism; monomorphism; pro-homotopy; shape; proper homotopy; pro-category
UR - http://eudml.org/doc/212393
ER -

References

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