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Images directes cohomologiques dans les catégories de modèles

Denis-Charles Cisinski (2003)

Annales mathématiques Blaise Pascal

Ces notes sont consacrées à la construction des limites homotopiques, et plus généralement, des images directes cohomologiques dans une catégorie de modèles arbitraire admettant des petites limites projectives. En outre, la théorie des dérivateurs de Grothendieck est introduite, à la fois en tant que motivation pour l’étude de telles structures, et en tant qu’outil de démonstration.

Induced mappings of homology decompositions

Martin Arkowitz (1998)

Banach Center Publications

We give conditions for a map of spaces to induce maps of the homology decompositions of the spaces which are compatible with the homology sections and dual Postnikov invariants. Several applications of this result are obtained. We show how the homotopy type of the (n+1)st homology section depends on the homotopy type of the nth homology section and the (n+1)st homology group. We prove that all homology sections of a co-H-space are co-H-spaces, all n-equivalences of the homology decomposition are...

Injective comodules and Landweber exact homology theories

Mark Hovey (2007)

Fundamenta Mathematicae

We classify the indecomposable injective E(n)⁎E(n)-comodules, where E(n) is the Johnson-Wilson homology theory. They are suspensions of the J n , r = E ( n ) ( M r E ( r ) ) , where 0 ≤ r ≤ n, with the endomorphism ring of J n , r being E ( r ) ^ * E ( r ) ^ , where E ( r ) ^ denotes the completion of E(r).

Injective models of G -disconnected simplicial sets

Marek Golasiński (1997)

Annales de l'institut Fourier

We generalize the results by G.V. Triantafillou and B. Fine on G -disconnected simplicial sets. An existence of an injective minimal model for a complete 𝕀 -algebra is presented, for any E I -category 𝕀 . We then make use of the E I -category 𝒪 ( G , X ) associated with a G -simplicial set X to apply these results to the category of G -simplicial sets.Finally, we describe the rational homotopy type of a nilpotent G -simplicial set by means of its injective minimal model.

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