Related papers: A note on stable recollements
We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform, coinductive way. The setup captures rewrite sequences of arbitrary ordinal length, but it has…
In this paper we study the structure of completions of symplectic reflection algebras. Our results provides a reduction to smaller algebras. We apply this reduction to the study of two-sided ideals and Harish-Chandra bimodules.
Given a monoidal $\infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them.…
Order-preserving pattern matching was introduced recently but it has already attracted much attention. Given a reference sequence and a pattern, we want to locate all substrings of the reference sequence whose elements have the same…
We demonstrate that an equivalence of categories using $\varepsilon$-interleavings as a fundamental component exists between the model of persistence modules as graded modules over a polynomial ring and the model of persistence modules as…
We verify a confluence result for the rewriting calculus of the linear category introduced in our previous paper. Together with the termination result proved therein, the generalized coherence theorem for linear category is established.…
While most research in Gold-style learning focuses on learning formal languages, we consider the identification of computable structures, specifically equivalence structures. In our core model the learner gets more and more information…
Persistent homology enables fast and computable comparison of topological objects. However, it is naturally limited to the analysis of topological spaces. We extend the theory of persistence, by guaranteeing robustness and computability to…
From certain triangle functors, called non-negative functors, between the bounded derived categories of abelian categories with enough projective objects, we introduce their stable functors which are certain additive functors between the…
Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term…
In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…
We show that the comma category $(\mathcal{F}\downarrow\mathbf{Grp})$ of groups under the free group functor $\mathcal{F}: \mathbf{Set} \to \mathbf{Grp}$ contains the category $\mathbf{Gph}$ of simple graphs as a full coreflective…
A full subcategory of a Grothendieck category is called deconstructible if it consists of all transfinite extensions of some set of objects. This concept provides a handy framework for structure theory and construction of approximations for…
Simple-minded systems of objects in a stable module category are defined by common properties with the set of simple modules, whose images under stable equivalences do form simple-minded systems. Over a representation-finite self-injective…
We provide an explicit procedure to glue (not necessarily compact) silting objects along recollements of triangulated categories with coproducts having a 'nice' set of generators, namely, well generated triangulated categories. This…
We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show…
We consider the equivalence from the stable module category to a subcategory $\mathcal{L}_A$ of the homotopy category constructed by Kato. This equivalence induces a correspondence between distinguished triangles in the homotopy category…
We establish a formal correspondence between resource calculi an appropriate linear multicategories. We consider the cases of (symmetric) representable, symmetric closed and autonomous multicategories. For all these structures, we prove…
We give a detailed proof of the following fundamental result: the singularity category of a ring is triangle equivalent to the stabilization of its stable module category. The result yields singular equivalences between rings of different…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…