Zobrazeno 1 - 10
of 60
pro vyhledávání: '"ALDROVANDI, ETTORE"'
Autor:
Aldrovandi, Ettore, Gunjal, Milind
We study monoidal 2-categories and bicategories in terms of categorical extensions and the cohomological data they determine in appropriate cohomology theories with coefficients in Picard groupoids. In particular, we analyze the hierarchy of possible
Externí odkaz:
http://arxiv.org/abs/2411.10530
Autor:
Aldrovandi, Ettore, Lester, Cynthia
Publikováno v:
Theory and Applications of Categories, Vol. 39, 2023, No. 27, pp 769-803
We extend Deligne's notion of determinant functor to tensor triangulated categories. Specifically, to account for the multiexact structure of the tensor, we define a determinant functor on the 2-multicategory of triangulated categories and we provide
Externí odkaz:
http://arxiv.org/abs/2305.02293
Publikováno v:
Homology, Homotopy and Applications 2022
Let $\pi: X \to S$ be a family of smooth projective curves, and let $L$ and $M$ be a pair of line bundles on $X$. We show that Deligne's line bundle $\langle{L,M}\rangle$ can be obtained from the $\mathcal{K}_2$-gerbe $G_{L,M}$ constructed in a previ
Externí odkaz:
http://arxiv.org/abs/2101.00044
Publikováno v:
J. of Algebra 505 (2018) 456-481
We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of extensions
Externí odkaz:
http://arxiv.org/abs/1711.05156
We define higher categorical invariants (gerbes) of codimension two algebraic cycles and provide a categorical interpretation of the intersection of divisors on a smooth proper algebraic variety. This generalization of the classical relation between
Externí odkaz:
http://arxiv.org/abs/1510.01825
Autor:
Aldrovandi, Ettore
Publikováno v:
Theory and Applications of Categories 30 (2015), 1256-1286
We show that $\mathit{ann}$-categories admit a presentation by crossed bimodules, and prove that morphisms between them can be expressed by special kinds spans between the presentations. More precisely, we prove the groupoid of morphisms between two
Externí odkaz:
http://arxiv.org/abs/1501.07592
Autor:
Aldrovandi, Ettore
Publikováno v:
Theory and Applications of Categories 32 (2017), 889--969
We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of the kind o
Externí odkaz:
http://arxiv.org/abs/1501.04664
Autor:
ALDROVANDI, ETTORE1 aldrovandi@math.fsu.edu, RAMACHANDRAN, NIRANJAN2 atma@math.umd.edu
Publikováno v:
Homology, Homotopy & Applications. 2023, Vol. 25 Issue 1, p21-51. 31p.
Autor:
Aldrovandi, Ettore, Tatar, Ahmet Emin
The weak units of strict monoidal 1- and 2-categories are already defined. In this paper, we define them for group-like 1- and 2-stacks. We show that they form a contractible Picard 1- and 2-stack, respectively. We give their cohomological descriptio
Externí odkaz:
http://arxiv.org/abs/1108.1922
Autor:
Aldrovandi, Ettore, Noohi, Behrang
Publikováno v:
Advances in Mathematics 225 (2010), 922-976
We study torsors over 2-groups and their morphisms. In particular, we study the first non-abelian cohomology group with values in a 2-group. Butterfly diagrams encode morphisms of 2-groups and we employ them to examine the functorial behavior of non-
Externí odkaz:
http://arxiv.org/abs/0909.3350