2 citations · 6 across the 11 of their papers we have counts for
12 papers
An example of the non-existence of coequalizers in the category of the A-categories
Mattia Ornaghi
We prove that the categories of strictly unital (resp.\ non unital) A-algebras and A-categories, with strictly unital (resp.\ non unital) A-morphis…
New examples of non-Fourier-Mukai exact functors via non-isomorphic octahedra
Alberto Canonaco, Mattia Ornaghi
We study a triangulated category that admits a full and strong exceptional sequence of three objects with one-dimensional Hom spaces. We show that the isomorphism clas…
A model structure on the category of A-categories with strict morphisms
Mattia Ornaghi
We prove that the category of (strictly unital) A-categories, linear over a commutative ring , with strict A-morphisms has a cofibrantly generated model struct…
A remark on fibrancy of ($\mbox{A$_{\infty}$Cat}$,$W^{\tiny\mbox{A}_{\infty}}_{\tiny\mbox{qe}}$)
Xiaofa Chen, Mattia Ornaghi
In this note we prove the existence, in the category of (strictly unital) Acategories, of the pullback of a (strictly unital) Afunctor, satisfying a particula…
Tensor product of A-categories
Mattia Ornaghi
In this paper we define the tensor product of two A-categories and two A-functors. This tensor product makes the category of A-categories symmetric…
The Homotopy Theory of Categories
Mattia Ornaghi
In this paper we describe the homotopy category of the categories. To do that we introduce the notion of semi-free category, which plays the role of standard co…
Localizations of the categories of categories and internal Homs over a ring
Alberto Canonaco, Mattia Ornaghi, Paolo Stellari
We show that, over an arbitrary commutative ring, the localizations of the categories of dg categories, of cohomologically unital, of unital and of strictly unital categ…
Rigid Dualizing Complexes over Commutative Rings and their Functorial Properties
Mattia Ornaghi, Saurabh Singh, Amnon Yekutieli
In this paper we treat Grothendieck Duality for noetherian rings via rigid dualizing complexes. In particular, we prove that every ring, essentially finite type over a regular base…
Localizations of the category of categories and internal Homs
Alberto Canonaco, Mattia Ornaghi, Paolo Stellari
We prove that the localizations of the categories of dg categories, of cohomologically unital and strictly unital categories with respect to the corresponding classes of…
A descent criterion for equivalences between equivariant derived categories
Francesco Amodeo, Riccardo Moschetti, Mattia Ornaghi
We investigate equivalences between the categories of perfects complexes of the quotients of two smooth projective schemes by the action of a finite group. As a result we give a ne…
Voevodsky's conjecture for cubic fourfolds and Gushel-Mukai fourfolds via noncommutative K3 surfaces
Mattia Ornaghi, Laura Pertusi
In the first part of this paper we will prove the Voevodsky's nilpotence conjecture for smooth cubic fourfolds and ordinary generic Gushel-Mukai fourfolds. Then, making use of nonc…
Some properties of the A-nerve
Mattia Ornaghi
The aim of this paper is to prove that the A-nerve of two quasi-equivalent A-categories (linear over a commutative ring) are weak-equivalent in the Joyal mode…