Related papers: Deformation Theory for $(\infty,n)$-categories
The Lie algebra specified by space of local functionals with commutator determined by the Gardner bracket was under survey. Problem of classification of deformations of this bracket over local infinitesimal transformations of functionals…
Huybrechts and Thomas recently constructed relative obstruction theory of objects of the derived category of coherent sheaves over smooth projective family. In this paper, we use this construction to obtain the absolute…
This work explores the deformation theory of algebraic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy…
Given a holomorphic Hermitian vector bundle and a star-product with separation of variables on a pseudo-Kaehler manifold, we construct a star product on the sections of the endomorphism bundle of the dual bundle which also has the…
We investigate higher-order geometric $k$-splines for template matching on Lie groups. This is motivated by the need to apply diffeomorphic template matching to a series of images, e.g., in longitudinal studies of Computational Anatomy. Our…
We give an elementary description of $2$-categories $\mathbf{Cat}\left(\mathcal{E}\right)$ of internal categories, functors and natural transformations, where $\mathcal{E}$ is a category modelling Lawvere's elementary theory of the category…
We introduce the notion of $\mathbb{E}_\infty$-descendability as well as a derived variant. We prove that several classes of descendable maps of commutative rings are $\mathbb{E}_\infty$-descendable. As an application, we prove a variant of…
We develop category-theoretic framework for universal homogeneous objects, with some applications in the theory of Banach spaces, linear orderings, and in topology of compact spaces.
For an endofunctor $F\colon\mathcal{C}\to\mathcal{C}$ on an ($\infty$-)category $\mathcal{C}$ we define the $\infty$-category $\operatorname{Cart}(\mathcal{C},F)$ of generalized Cartier modules as the lax equalizer of $F$ and the identity.…
Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…
An orientation theory for flow categories without bubbling is determined by a functor of $\infty$-categories $\mu \colon \mathcal{C} \to U/O$. For any such functor, we construct a stable $\infty$-category $\mathcal{F}low^{\mu}$ of…
Homotopic morphisms of $\mathbb E$-triangles in extriangulated categories are introduced. Any morphism of $\mathbb E$-triangles is a composition of homotopic morphisms. Any morphism $(\alpha_1, \alpha_2, \alpha_3)$ of $\mathbb E$-triangles…
An n-category is some sort of algebraic structure consisting of objects, morphisms between objects, 2-morphisms between morphisms, and so on up to n-morphisms, together with various ways of composing them. We survey various concepts of…
The bulk of this paper is devoted to the comparison of several models for the theory of (infinity,2)-categories: that is, higher categories in which all k-morphisms are invertible for k > 2 (the case of (infinity,n)-categories is also…
This is the first of a series of papers to construct the deformation theory of the form Schr\"odinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a noncompact complete K\"ahler manifold with bounded…
We completely characterize the unimodal category for functions $f:\mathbb R\to[0,\infty)$ using a decomposition theorem obtained by generalizing the sweeping algorithm of Baryshnikov and Ghrist. We also give a characterization of the…
For a symplectic manifold satisfying some topological condition,we define a special class of modules over the deformation quantization algebra. For any two such modules we construct an infinity local system of morphisms. We construct such…
We show that the equivariant $E$-theory category $\mathrm{E}_{\mathrm{sep}}^{G}$ for separable $C^{*}$-algebras is a compactly assembled stable $\infty$-category. We derive this result as a consequence of the shape theory for…
This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their…
The primary goal of this paper is to abstract notions, results and constructions from the theory of categories to the broader setting of plots. Loosely speaking, a plot can be thought of as a non-associative non-unital category with a…