3,101 research outputs found
On the loop space of a 2-category
Every small category has a classifying space 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 of a 2-category and prove that, under
certain conditions, the loop space 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 artÃculo 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
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