Displaying similar documents to “Relative epimorphisms and monomorphisms in homotopy theory”

On some weak monomorphisms and weak epimorphisms of pro-HTop*.

I. Pop (1996)

Revista Matemática de la Universidad Complutense de Madrid

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Related to Shape Theory, in a previous paper (1992) we studied weak monomorphisms and weak epimorphisms in the category of pro-groups. In this note we give some intrinsic characterizations of the weak monomorphisms and the weak epimorphisms in pro-HTop* in the case when one of the two objects of such a morphism is a rudimentary system.

Cochains and homotopy type

Michael A. Mandell (2006)

Publications Mathématiques de l'IHÉS

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Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category of E algebras is faithful but not full.

Exploring W.G. Dwyer's tame homotopy theory.

Hans Scheerer, Daniel Tanré (1991)

Publicacions Matemàtiques

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Let S be the category of r-reduced simplicial sets, r ≥ 3; let L be the category of (r-1)-reduced differential graded Lie algebras over Z. According to the fundamental work [3] of W.G. Dwyer both categories are endowed with closed model category structures such that the associated tame homotopy category of S is equivalent to the associated homotopy category of L. Here we embark on a study of this equivalence and its implications. In particular, we show how to compute homology, cohomology,...