Homotopy theory for (braided) cat-groups
Antonio R. Garzon, Jesus G. Miranda (1997)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Displaying similar documents to “Homotopy groups of small categories and derived functors”
Homotopy theory for (braided) cat-groups
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Category with a natural cone
Francisco Díaz, Sergio Rodríguez-Machín (2006)
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Generally, in homotopy theory a cylinder object (or, its dual, a path object) is used to define homotopy between morphisms, and a cone object is used to build exact sequences of homotopy groups. Here, an axiomatic theory based on a cone functor is given. Suspension objects are associated to based objects and cofibrations, obtaining homotopy groups referred to an object and relative to a cofibration, respectively. Exact sequences of these groups are built. Algebraic and particular examples...
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Hans Scheerer, Daniel Tanré (1991)
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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. ...