58 citations · 177 across the 12 of their papers we have counts for
12 papers
Lie Groupoids
Henrique Bursztyn, Matias del Hoyo
A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoi…
Higher Vector Bundles
Matias del Hoyo, Giorgio Trentinaglia
We introduce higher analogs for cleavages in the context of (Kan) simplicial fibrations. We apply them to obtain geometric models for representations up to homotopy of (higher) Lie…
Poisson double structures
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We…
The general linear 2-groupoid
Matias del Hoyo, Davide Stefani
We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem exp…
Morita equivalences of vector bundles
Matias del Hoyo, Cristian Ortiz
We study vector bundles over Lie groupoids, known as VB-groupoids, and their induced geometric objects over differentiable stacks. We establish a fundamental theorem that character…
Riemannian metrics on differentiable stacks
Matias del Hoyo, Rui Loja Fernandes
We study Riemannian metrics on Lie groupoids in the relative setting. We show that any split fibration between proper groupoids can be made Riemannian, and we use these metrics to…
Complete connections on fiber bundles
Matias del Hoyo
Every smooth fiber bundle admits a complete (Ehresmann) connection. This result appears in several references, with a proof on which we have found a gap, that does not seem possibl…
Vector bundles over Lie groupoids and algebroids
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucid…
Riemannian metrics on Lie groupoids
Matias L. del Hoyo, Rui Loja Fernandes
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, incl…
On the loop space of a 2-category
Matias L. del Hoyo
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 cat…
On the subdivision of small categories
Matias Luis del Hoyo
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we dedu…
Classical invariants for global actions and groupoid atlases
Matias Luis del Hoyo, Elias Gabriel Minian
A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the conce…