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Dive into the research topics where M. Bullejos is active.

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Featured researches published by M. Bullejos.


K-theory | 2003

On the Geometry of 2-Categories and their Classifying Spaces

M. Bullejos; Antonio M. Cegarra

In this paper we prove that realizations of geometric nerves are classifying spaces for 2-categories. This result is particularized to strict monoidal categories and it is also used to obtain a generalization of Quillens Theorem A.


Journal of Pure and Applied Algebra | 1993

On catn-groups and homotopy types☆

M. Bullejos; Antonio M. Cegarra; J. Duskin

Abstract We give an algebraic proof of Lodays ‘Classification theorem’ for truncated homotopy types. In particular we give a precise construction of the homotopy cat n -group associated to a pointed topological space which is based on the use of the internal fundamental groupoid functor together with Illusies ‘total Dec’.


Journal of Pure and Applied Algebra | 1987

Higher dimensional obstruction theory in algebraic categories

Antonio M. Cegarra; M. Bullejos; Antonio R. Garzón

In this paper we generalize Duskins low dimensional obstruction theory, established for the Barr-Becks cotriple cohomogy HG2, to higher dimensions by giving a new interpretation of HGn+1 in terms of obstructions to the existence of non-singular n-extensions or realizations to n-dimensional abstract kernels. We find a surjective map Obs from the set of all n-dimensional abstract kernels with center a fixed S-module A to HGn+1(S,A) in such a way that an abstract kernel has a realization if and only if its obstruction vanishes, the set of equivalence classes of such realizations being in this case a principal homogeneous space over HGn(S,A).


Mathematics of Computation | 2008

Proportionally modular diophantine inequalities and the Stern-Brocot tree

M. Bullejos; J. C. Rosales

Given positive integers a, b and c to compute a generating system for the numerical semigroup whose elements are all positive integer solutions of the inequality ax mod b < cx is equivalent to computing a Bezout sequence connecting two reduced fractions. We prove that a proper Bezout sequence is completely determined by its ends and we give an algorithm to compute the unique proper Bezout sequence connecting two reduced fractions. We also relate Bezout sequences with paths in the Stern-Brocot tree and use this tree to compute the minimal positive integer solution of the above inequality.


Applied Categorical Structures | 2005

A FULL AND FAITHFUL NERVE FOR 2-CATEGORIES

M. Bullejos; E. Faro; Víctor Blanco

The notion of geometric nerve of a 2-category (Street, J. Pure Appl. Algebra49 (1987), 283–335) provides a full and faithful functor if regarded as defined on the category of 2-categories and lax 2-functors. Furthermore, lax 2-natural transformations between lax 2-functors give rise to homotopies between the corresponding simplicial maps. These facts allow us to prove a representation theorem of the general non-abelian cohomology of groupoids (classifying non-abelian extensions of groupoids) by means of homotopy classes of simplicial maps.


Journal of Pure and Applied Algebra | 1998

On the equivariant 2-type of a G-space☆

M. Bullejos; J.G. Cabello; E. Faro

Abstract A classical theorem of Mac Lane and Whitehead states that the homotopy type of a topological space with trivial homotopy at dimensions 3 and greater can be reconstructed from its π1 and π2, and a cohomology class k3 /gE H3(π1, π2). More recently, Moerdijk and Svensson suggested the possibility of using Bredon cohomology to extend this result to the equivariant case, that is, for spaces X equipped with an action by a fixed group G. In this paper we carry out this suggestion and prove an analogue of the classical result in the equivariant case.


Journal of Algebra | 1990

Cohomology and Higher Dimensional Baer Invariants

Antonio M. Cegarra; M. Bullejos

In this paper we work in a categorical setting which includes the most usual algebraic categories, for example, groups, rings (associative, com- mutative), or algebras (associative, commutative, Jordan, Lie, etc.). Such a setting is supplied by the theory of Q-groups in the sense of Higgins [S]. Let 9 be a variety of Q-groups and g E 9 a subvariety, with associated quotient functor U: 9 + 99. Several authors have shown that the first Baer invariant of an object A in 9, g,(A) = L, U(A), plays an important role in the study of the relationship between extensions of U(A) in the subvariety &J and general extensions of


Canadian Journal of Mathematics | 1991

A

M. Bullejos; Antonio M. Cegarra


Cahiers de Topologie et Géométrie Différentielle Catégoriques | 2003

3

M. Bullejos; E. Faro; M.A. García-Muñoz


Mathematische Zeitschrift | 2005

-dimensional nonabelian cohomology of groups with applications to homotopy classification of continuous maps

Víctor Blanco; M. Bullejos; E. Faro

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A. Lirola

University of Granada

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