Related papers: The Glueing Construction and Double Categories
In this paper we develop the theory of Artin-Wraith glueings for topological spaces. As an application, we show that some categories of compactifications of coarse spaces that agree with the coarse structures are invariant under coarse…
Artin glueings of frames correspond to adjoint split extensions in the category of frames and finite-meet-preserving maps. We extend these ideas to the setting of toposes and show that Artin glueings of toposes correspond to a 2-categorical…
We use double categories to obtain a single theorem characterizing certain exponentiable morphisms of small categories, topological spaces, locales, and posets.
Artin glueings provide a way to reconstruct a frame from a closed sublocale and its open complement. We show that Artin glueings can be described as the weakly Schreier split extensions in the category of frames with finite-meet preserving…
In this article, we develop a general technique for gluing subcategories of $\infty$-categories. We obtain categorical equivalences between simplicial sets associated to certain multisimplicial sets. Such equivalences can be used to…
For an abelian tensor category a stack is constructed. As an application we show that our construction can be used to recover a quasi-compact separated scheme from the category of its quasi-coherent sheaves. In another application, we show…
Given a particular collection of categorical axioms, aimed at capturing properties of the category of locales, we show that if $\mathcal{C}$ is a category that satisfies the axioms then so too is the category $[ G, \mathcal{C}]$ of…
In this paper we discuss the sufficient and necessary conditions for multiple Alexandrov spaces being glued to an Alexandrov space. We propose a Gluing Conjecture, which says that the finite gluing of Alexandrov spaces is an Alexandrov…
We introduce and describe the $2$-category $\mathsf{Grt}_{\flat}$ of Grothendieck categories and flat morphisms between them. First, we show that the tensor product of locally presentable linear categories $\boxtimes$ restricts nicely to…
We consider categories of generalized perverse sheaves, with relaxed constructibility conditions, by means of the process of gluing $t$-structures and we exhibit explicit abelian categories defined in terms of standard sheaves categories…
We introduce an analogue to the amalgamation of metric spaces into the setting of Lorentzian pre-length spaces. This provides a very general process of constructing new spaces out of old ones. The main application in this work is an…
We prove that an arbitrary countable dimensional Lie algebra over a field of characteristic $\neq 2$ that is locally of subexponential growth is embeddable in a finitely generated Lie algebra of subexponential growth.
Recently, Wang, Wei and Zhang define the recollement of extriangulated categories, which is a generalization of both recollement of abelian categories and recollement of triangulated categories. For a recollement $(\mathcal A ,\mathcal…
We develop a gluing algorithm for Gromov-Witten invariants of toric Calabi-Yau threefolds based on localization and gluing graphs. The main building block of this algorithm is a generating function of cubic Hodge integrals of special form.…
The multiplicative fragment of Linear Logic is the formal system in this family with the best understood proof theory, and the categorical models which best capture this theory are the fully complete ones. We demonstrate how the Hyland-Tan…
Cobordism categories are known to be compact closed. They can therefore be used to define non-degenerate models of multiplicative linear logic by combining the Int construction with double glueing. In this work we detail such construction…
This paper is a follow-up to arXiv:2407.08471. Let $X$ be a a $(-1)$-shifted symplectic derived Deligne--Mumford stack. Thanks to the Darboux lemma of Brav--Bussi--Joyce, $X$ is locally modeled by derived critical loci of a function $f$ on…
We provide a formulation of the univalence axiom in a universe category model of dependent type theory that is convenient to verify in homotopy-theoretic settings. We further develop a strengthening of the univalence axiom, called pointed…
From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…
We introduce a notion of gluability for poset-indexed Bridgeland slicings on triangulated categories and show how a gluing abelian slicing on the heart of a bounded $t$-structure naturally induces a family of perverse $t$-structures. Our…