Antonio Martinez Cegarra

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Papers by Antonio Martinez Cegarra

arXiv (Cornell University), Jul 6, 2009

arXiv: K-Theory and Homology, 2016

Leech's (co)homology groups of finite cyclic monoids are computed.

We introduce and study hypercrossed complexes of Lie algebras, that is, non-negatively graded cha... more We introduce and study hypercrossed complexes of Lie algebras, that is, non-negatively graded chain complexes of Lie algebras L = (Ln, ∂n) endowed with an additional structure by means of a suitable set of bilinear maps Lr × Ls → Ln. The Moore complex of any simplicial Lie algebra acquires such a structure and, in this way, we prove a Dold-Kan type equivalence between the category of simplicial Lie algebras and the category of hypercrossed complexes of Lie algebras. Several consequences of examining particular classes of hypercrossed complexes of Lie algebras are presented.

Mathematics, 2020

This paper deals with well-known weak homotopy equivalences that relate homotopy colimits of smal... more This paper deals with well-known weak homotopy equivalences that relate homotopy colimits of small categories and simplicial sets. We show that these weak homotopy equivalences have stronger cohomology-preserving properties than for local coefficients.

Mathematics, 2020

The purpose of this work is to extend Leech cohomology for monoids (and so Eilenberg-Mac Lane coh... more The purpose of this work is to extend Leech cohomology for monoids (and so Eilenberg-Mac Lane cohomology of groups) to presheaves of monoids on an arbitrary small category. The main result states and proves a cohomological classification of monoidal prestacks on a category with values in groupoids with abelian isotropy groups. The paper also includes a cohomological classification for extensions of presheaves of monoids, which is useful to the study of H -extensions of presheaves of regular monoids. The results apply directly in several settings such as presheaves of monoids on a topological space, simplicial monoids, presheaves of simplicial monoids on a topological space, monoids or simplicial monoids on which a fixed monoid or group acts, and so forth.