# 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

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topDydak, 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 -

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