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Une formule pour les extensions de foncteurs composés

Alain Troesch (2003)

Fundamenta Mathematicae

Let p be a prime, and let ℱ be the category of functors from the finite p -vector spaces to all p -vector spaces. The object Id of ℱ is the inclusion functor. Let F and G be two objects in ℱ. If F and G satisfy suitable conditions, the main result of this paper allows one to compute E x t * ( I d , G F ) from the knowledge of E x t * ( I d , F ) and E x t * ( I d , G ) .

Une opérade anticyclique sur les arbustes

Frédéric Chapoton (2010)

Annales mathématiques Blaise Pascal

We define new combinatorial objects, called shrubs, such that forests of rooted trees are shrubs. We then introduce a structure of operad on shrubs. We show that this operad is contained in the Zinbiel operad, by using the inclusion of Zinbiel in the operad of moulds. We also prove that this inclusion is compatible with the richer structure of anticyclic operad that exists on Zinbiel and on moulds.

Une résolution injective des puissances symétriques tordues

Alain Troesch (2005)

Annales de l’institut Fourier

Dans cet article, on construit une résolution injective explicite des puissances symétriques tordues S * ( j ) dans la catégorie des foncteurs strictement polynomiaux. Cette construction généralise à toute caractéristique la construction donnée par Friedlander et Suslin en caractéristique 2.

Uniform filters

Manuel Garcia Román, Mercedes Márquez Hernández, Pascual Jara, Alain Verschoren (1999)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Uniformly Movable Categories and Uniform Movability of Topological Spaces

P. S. Gevorgyan, I. Pop (2007)

Bulletin of the Polish Academy of Sciences. Mathematics

A categorical generalization of the notion of movability from inverse systems and shape theory was given by the first author who defined the notion of movable category and used it to interpret the movability of topological spaces. In this paper the authors define the notion of uniformly movable category and prove that a topological space is uniformly movable in the sense of shape theory if and only if its comma category in the homotopy category HTop over the subcategory HPol of polyhedra is uniformly...

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