Displaying similar documents to “Model-categories of coalgebras over operads.”

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,...

Non functorial cylinders in a model category

J. García-Calcines, P. García-Díaz, S. Rodríguez-Machín (2006)

Open Mathematics

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Taking cylinder objects, as defined in a model category, we consider a cylinder construction in a cofibration category, which provides a reformulation of relative homotopy in the sense of Baues. Although this cylinder is not a functor we show that it verifies a list of properties which are very closed to those of an I-category (or category with a natural cylinder functor). Considering these new properties, we also give an alternative description of Baues’ relative homotopy groupoids. ...