Antonio Martínez Cegarra

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The long-known results of Schreier on group extensions are here raised to a categorical level by giving a factor set theory for torsors under a categorical group (G, ⊗) over a small category B. We show a natural bijection between the set of equivalence classes of such torsors and [B(B), B(G, ⊗)], the set of homotopy classes of continuous maps between the(More)
The problem of extending categories by groups, including theory of obstructions, is studied by means of factor systems and various homological invariants, generalized from Schreier– Eilenberg–Mac Lane group extension theory. Explicit applications are then given to the classi-ÿcation of several algebraic constructions long known as crossed products,(More)
This paper explores the relationship amongst the various simpli-cial and pseudo-simplicial objects characteristically associated to any bicate-gory C. It proves the fact that the geometric realizations of all of these possible candidate 'nerves of C' are homotopy equivalent. Any one of these realizations could therefore be taken as the classifying space BC(More)
The long-known results of Schreier᎐Eilenberg᎐Mac Lane on group extensions are raised to a categorical level, for the classification and construction of the manifold of all graded monoidal categories, the type being given group ⌫ with 1-component a given monoidal category. Explicit application is made to the classification of strongly graded bialgebras over(More)
This work contributes to clarifying several relationships between certain higher categorical structures and the homotopy type of their classifying spaces. Bicategories (in particular monoidal categories) have well understood simple geometric realizations, and we here deal with homotopy types represented by lax diagrams of bicategories, that is, lax functors(More)