On the loop space of a 2-category

Every small category $C$ has a classifying space $BC$ associated in a natural way. This construction can be extended to other contexts and set up a fruitful interaction between categorical structures and homotopy types. In this paper we study the classifying space $B_2C$ of a 2-category $C$ and prove that, under certain conditions, the loop space $\Omega_c B_2C$ can be recovered up to homotopy from the endomorphisms of a given object. We also present several subsidiary results that we develop to prove our main theorem.Comment: 21 pages, final version. Section 8 concerning the main theorem was rewritten. In particular, a partial converse for the main theorem was adde

Riemannian metrics on Lie groupoids

We introduce a notion of metric on a Lie groupoid, compatible with multiplication, and we study its properties. We show that many families of Lie groupoids admit such metrics, including the important class of proper Lie groupoids. The exponential map of these metrics allow us to establish a Linearization Theorem for Riemannian groupoids, obtaining both a simpler proof and a stronger version of the Weinstein-Zung Linearization Theorem for proper Lie groupoids. This new notion of metric has a simplicial nature which will be explored in future papers of this series.Comment: 29 pages; Final version accepted for publication in Journal f\"ur die reine und angewandte Mathematik (Crelle

Nuevo documento metróaco hallado en la provincia de Segovia

Se presenta en este articulo un ara votiva inédidta de la provincia de Segovia, que reviste sumo interés tanto desde el punto de vista formal como del contenido, resultando de inapreciable valor para lingüistas e historiadores. Dadas las dificultades de interpretación, mas que de lectura, de alguna secuencia, consideramos que se trata de un primer estudio o presentación de la pieza, que dará lugar a posteriores trabajos, sin duda mas completos y acabados, sobre religiosidad, romanización de la submeseta norte, etc

Cvrsv certari : acerca de la afición cinegética de Q. Tvllivs Maximvs (CIL II 2660)

Presentamos en este artículo un nuevo estudio de las cinco inscripciones que E. Hübner reunió bajo el núm. CIL II 2660, con nueva edición de texto y nueva interpretación.In this paper the author offers a new study about the five latin inscriptions that E. Hübner published in CIL II 2660, with a new edition and a new interpretation