Related papers: Coaction functors, II
We present a systematic study of the structure of crossed products and fixed point algebras by compact group actions with the Rokhlin property on not necessarily unital C*-algebras. Our main technical result is the existence of an…
We will study commuting properties of the defect functor $\mathrm{Dev}_\beta=\mathrm{Coker}\mathrm{Hom}_\mathcal{C}(\beta,-)$ associate to a homomorphism $\beta$ in a finitely presented category. As an application, we characterize objects…
We consider the category of comodules over a smash coproduct coalgebra $C\smashco H$. We show that there is a Grothendieck spectral sequence connecting the derived functors of the Hom functors coming from $C\smashco H$-colinear,…
It is well-known that pseudo functors from bicategories of spans are equivalent to Beck-Chevalley bifibrations, and therefore capture the relationships underlying the adjunctions suitable as semantics for existential quantification. This…
We provide an equivariant extension of the bivariant Cuntz semigroup introduced in previous work for the case of compact group actions over C*-algebras. Its functoriality properties are explored and some well-known classification results…
We generalize a result, on the pro-representability of Milnor $K$-cohomology groups at the identity, that's due to Bloch. In particular, we prove, for $X$ a smooth, proper, and geometrically connected variety defined over an algebraic field…
In this paper, we introduce a property of topological dynamical systems that we call finite dynamical complexity. For systems with this property, one can in principle compute the $K$-theory of the associated crossed product $C^*$-algebra by…
We generalize the construction of reflection functors from classical representation theory of quivers to arbitrary small categories with freely attached sinks or sources. These reflection morphisms are shown to induce equivalences between…
A strong version of the quantization conjecture of Guillemin and Sternberg is proved. For a reductive group action on a smooth, compact, polarized variety (X,L), the cohomologies of L over the GIT quotient X // G equal the invariant part of…
This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…
We investigate approximation properties for $C^*$-algebras and their crossed products by actions and coactions by locally compact groups. We show that Haagerup's approximation constant is preserved for crossed products by arbitrary amenable…
Let $\mathfrak{a}$ be an ideal in a commutative ring $R$. For an $R$-module $M$, we consider the small $\mathfrak{a}$-torsion $\Gamma_{\mathfrak{a}}(M)=\{x\in M\mid\exists n\in\mathbb{N}:\mathfrak{a}^n\subseteq(0:_Rx)\}$ and the large…
In this paper we develop homology and cohomology theories which play the same role for real projective varieties that Lawson homology and morphic cohomology play for projective varieties respectively. They have nice properties such as the…
We establish a precise relationship between functor calculus and the projective dimension of multipersistence modules. Specifically, we develop a new notion of functor calculus for functors from posets, which detects vanishing total fibers…
We prove an identity relating the product of two opposite Schubert varieties in the (equivariant) quantum K-theory ring of a cominuscule flag variety to the minimal degree of a rational curve connecting the Schubert varieties. We deduce…
We investigate scalar restriction, scalar extension, and scalar coextension functors for graded modules, including their interplay with coarsening functors, graded tensor products, and graded Hom functors. This leads to several…
With view to applications in stochastic analysis and geometry, we introduce a new correspondence for positive definite kernels (p.d.) $K$ and their associated reproducing kernel Hilbert spaces. With this we establish two kinds of…
We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various…
Let $F\colon \mathcal{C} \to \mathcal{E}$ be a functor from a category $\mathcal{C}$ to a homological (Borceux-Bourn) or semi-abelian (Janelidze-M\'arki-Tholen) category $\mathcal{E}$. We investigate conditions under which the homology of…
We prove gauge-invariant uniqueness theorems with respect to maximal and normal coactions for $C^*$-algebras associated to product systems of $C^*$-correspondences. Our techniques of proof are developed in the abstract context of Fell…