Geodesic
Bimorphisms in pro-homotopy and proper homotopy
Fundamenta Mathematicae, Tome 160 (1999) no. 3, pp. 269-286.

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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 $tow(H_0)$ is an isomorphism if Y is movable. Recall that $\tow(H_0)$ is the full subcategory of $pro-H_0$ consisting of inverse sequences in $H_0$, the homotopy category of pointed connected CW complexes.
DOI : 10.4064/fm-160-3-269-286
Keywords: epimorphism, monomorphism, pro-homotopy, shape, proper homotopy

Jerzy Dydak 1 ; Francisco Romero Ruiz del Portal 1

1 
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Jerzy Dydak; Francisco Romero Ruiz del Portal. Bimorphisms in pro-homotopy and proper homotopy. Fundamenta Mathematicae, Tome 160 (1999) no. 3, pp. 269-286. doi : 10.4064/fm-160-3-269-286. http://geodesic.mathdoc.fr/articles/10.4064/fm-160-3-269-286/

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