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In this paper we take up again the deformation theory for K -linear pseudofunctors initiated in Elgueta (Adv. Math. 182 (2004) 204–277). We start by introducing a notion of 2-cosemisimplicial object in an arbitrary 2-category and analyzing the corresponding coherence question, where the...
In this paper we consider the category of unstable modules over the Steenrod algebra. We prove the existence of finite primary decompositions in this category. Moreover, we prove the existence of Thom classes in noetherian unstable modules, i.e., elements that generate cyclic unstable submodules...
Quantum homogeneous supervector bundles arising from the quantum general linear supergoup are studied. The space of holomorphic sections is promoted to a left exact covariant functor from a category of modules over a quantum parabolic sub-supergroup to the category of locally finite modules of...
We introduce the notion of quadri-algebras. These are associative algebras for which the multiplication can be decomposed as the sum of four operations in a certain coherent manner. We present several examples of quadri-algebras: the algebra of permutations, the shuffle algebra, tensor products...
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