Polynomial functors over finite fields
Sets with two associative operations
In this paper we consider duplexes, which are sets with two associative binary operations. Dimonoids in the sense of Loday are examples of duplexes. The set of all permutations carries a structure of a duplex. Our main result asserts that it is a free duplex with an explicitly described set of generators. The proof uses a construction of the free duplex with one generator by planary trees.
On the corresponding to bialgebras
On Leibniz homology
We describe a spectral sequence for computing Leibniz cohomology for Lie algebras.
Hodge decomposition for higher order Hochschild homology
Ganea term for CCG-homology of crossed modules.
In [2] an internal homology theory of crossed modules was defined (CCG-homology for short), which is very much related to the homology of the classifying spaces of crossed modules ([5]). The goal of this note is to construct a low-dimensional homology exact sequence corresponding to a central extension of crossed modules, which is quite similar to the one constructed in [3] for group homology.
Spaces associated to quadratic endofunctors of the category of groups.
Square groups are gadgets classifying quadratic endofunctors of the category of groups. Applying such a functor to the Kan simplicial loop group of the 2-dimensional sphere, one obtains a one-connected three-type. We consider the problem of characterization of those three-types X which can be obtained in this way. We solve this problem in some cases, including the case when π(X) is a finitely generated abelian group. The corresponding stable problem is solved completely.
The Euler-Poincaré characteristic of a Lie algebra.
Groupoid enriched categories and natural systems.
Foncteurs polynomiaux et foncteurs de Mackey non linéaires
On décrit les foncteurs polynomiaux, des groupes abéliens libres vers les groupes abéliens, comme des diagrammes de groupes abéliens dont on explicite les relations.
Comparison of abelian categories recollements.
Linear extensions and nilpotence of Maltsev theories.
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