54 citations · 182 across the 24 of their papers we have counts for
13 papers · 1 filter
On Krull-Schmidt bicategories
Ivo Dell'Ambrogio
We study the existence and uniqueness of direct sum decompositions in additive bicategories. We find a simple definition of Krull-Schmidt bicategories, for which we prove the uniqu…
Cohomological Mackey 2-functors
Paul Balmer, Ivo Dell'Ambrogio
We show that the bicategory of finite groupoids and right-free permutation bimodules is a quotient of the bicategory of Mackey 2-motives introduced in arXiv:1808.04902, obtained by…
On the comparison of spans and bisets
Ivo Dell'Ambrogio, James Huglo
We compare the bicategory of spans with that of bisets (a.k.a. bimodules, distributors, profunctors) in the context of finite groupoids. We construct in particular a well-behaved p…
Green equivalences in equivariant mathematics
Paul Balmer, Ivo Dell'Ambrogio
We establish Green equivalences for all Mackey 2-functors, without assuming Krull-Schmidt. By running through the examples of Mackey 2-functors, we recover all variants of the Gree…
A note on triangulated monads and categories of module spectra
Ivo Dell'Ambrogio, Beren Sanders
Consider a monad on an idempotent complete triangulated category with the property that its Eilenberg-Moore category of modules inherits a triangulation. We show that any other tri…
Affine weakly regular tensor triangulated categories
Ivo Dell'Ambrogio, Donald Stanley
We prove that the Balmer spectrum of a tensor triangulated category is homeomorphic to the Zariski spectrum of its graded central ring, provided the triangulated category is genera…
Grothendieck-Neeman duality and the Wirthmüller isomorphism
Paul Balmer, Ivo Dell'Ambrogio, Beren Sanders
We clarify the relationship between Grothendieck duality à la Neeman and the Wirthmüller isomorphism à la Fausk-Hu-May. We exhibit an interesting pattern of symmetry in the existen…
Restriction to finite-index subgroups as étale extensions in topology, KK-theory and geometry
Paul Balmer, Ivo Dell'Ambrogio, Beren Sanders
For equivariant stable homotopy theory, equivariant KK-theory and equivariant derived categories, we show how restriction to a subgroup of finite index yields a finite commutative…
A Quillen model for classical Morita theory and a tensor categorification of the Brauer group
Ivo Dell'Ambrogio, Gonçalo Tabuada
Let K be a commutative ring. In this article we construct a symmetric monoidal Quillen model structure on the category of small K-categories which enhances classical Morita theory.…
Even more spectra: tensor triangular comparison maps via graded commutative 2-rings
Ivo Dell'Ambrogio, Greg Stevenson
We initiate the theory of graded commutative 2-rings, a categorification of graded commutative rings. The goal is to provide a systematic generalization of Paul Balmer's comparison…
Morita homotopy theory of C*-categories
Ivo Dell'Ambrogio, Goncalo Tabuada
In this article we establish the foundations of the Morita homotopy theory of C*-categories. Concretely, we construct a cofibrantly generated simplicial symmetric monoidal Quillen…
On the derived category of a graded commutative noetherian ring
Ivo Dell'Ambrogio, Greg Stevenson
For any graded commutative noetherian ring, where the grading group is abelian and where commutativity is allowed to hold in a quite general sense, we establish an inclusion-preser…
The unitary symmetric monoidal model category of small C*-categories
Ivo Dell'Ambrogio
We produce a cofibrantly generated simplicial symmetric monoidal model structure for the category of (small unital) C*-categories, whose weak equivalences are the unitary equivalen…