Related papers: Horizontal Linkage of Coherent Functors

We investigate correspondence functors, namely 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 specific properties which do not hold for…

A new homological symmetry condition is exhibited that extends and unifies several recently defined and widely used concepts. Applications include general constructions of tilting modules and derived equivalences, and characterisations of…

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new…

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 ring, has a unique rigid dualizing complex. The rigid…

We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give…

In the context of infinity categories, we rethink the notion of derived functor in terms of correspondences. This is especially convenient for the description of a passage from an adjoint pair (F,G) of functors to a derived adjoint pair…

Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs…

We present a study on the Yoneda-Dress construction of biset functors of linear representations over a field of characteristic zero. We give a characterization of their lattices of ideals and we provide a criterion of vanishing for their…

We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These…

We give a representation for entanglement-breaking channels in separable Hilbert space that generalizes the "Kraus decomposition with rank one operators" and use it to describe the complementary channels. We also give necessary and…

We introduce neural networks for end-to-end differentiable proving of queries to knowledge bases by operating on dense vector representations of symbols. These neural networks are constructed recursively by taking inspiration from the…

In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of preservation of positivity or monotonicity of functions for some models in approximation and interpolation…

Combining additive models and neural networks allows to broaden the scope of statistical regression and extend deep learning-based approaches by interpretable structured additive predictors at the same time. Existing attempts uniting the…

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…

We investigate the connection between left exact $\infty$-functors between finitely complete quasicategories and exact functors between fibration categories, describing a procedure to approximate flat $\infty$-functors of the former type by…

We study zeta functions enumerating submodules invariant under a given endomorphism of a finitely generated module over the ring of ($S$-)integers of a number field. In particular, we compute explicit formulae involving Dedekind zeta…

We define the notion of an indexed profunctor over a 2-category, and use it to develop an abstract theory of limits. The theory subsumes (conical) limits, weighted limits, ends and Kan extensions. Results include an abstract version of the…

We consider two endofunctors of the form $~F:X\longrightarrow M\otimes X~$, where $~M~$ is a non degenerate module, related to the unit interval and the Sierpinski gasket, and their final co-algebras. The functors are defined on the…

This paper develops a generalized cotangent-type series, extending classical expansions to higher-order lattice sums. By introducing a new family of series indexed by integer powers, we derive closed form representations that combine…

We consider the category of linear relations over an arbitrary commutative ring, and identify it as a subcategory of the category of Kronecker representations. We observe that this subcategory forms a definable, faithful and hereditary…