Zobrazeno 1 - 10
of 66
pro vyhledávání: '"Dyckerhoff, Tobias"'
We introduce notions of lax semiadditive and lax additive $(\infty,2)$-categories, categorifying the classical notions of semiadditive and additive 1-categories. To establish a well-behaved axiomatic framework, we develop a calculus of lax matrices a
Externí odkaz:
http://arxiv.org/abs/2402.12251
Euler's continuants are universal polynomials expressing the numerator and denominator of a finite continued fraction whose entries are independent variables. We introduce their categorical lifts which are natural complexes (more precisely, coherentl
Externí odkaz:
http://arxiv.org/abs/2306.13350
We study complexes of stable $\infty$-categories, referred to as categorical complexes. As we demonstrate, examples of such complexes arise in a variety of subjects including representation theory, algebraic geometry, symplectic geometry, and differe
Externí odkaz:
http://arxiv.org/abs/2301.02606
We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and equip it wi
Externí odkaz:
http://arxiv.org/abs/2106.02873
Constructible sheaves of abelian groups on a stratified space can be equivalently described in terms of representations of the exit-path category. In this work, we provide a similar presentation of the abelian category of perverse sheaves on a strati
Externí odkaz:
http://arxiv.org/abs/2012.11388
Publikováno v:
Forum of Mathematics, Sigma, vol. 9, p. e10, 2021
We show that the perfect derived categories of Iyama's $d$-dimensional Auslander algebras of type $\mathbb{A}$ are equivalent to the partially wrapped Fukaya categories of the $d$-fold symmetric product of the $2$-dimensional unit disk with finitely
Externí odkaz:
http://arxiv.org/abs/1911.11719
Publikováno v:
Algebr. Geom. Topol. 20 (2020) 3147-3182
In this work, we introduce a 2-categorical variant of Lurie's relative nerve functor. We prove that it defines a right Quillen equivalence which, upon passage to $\infty$-categorical localizations, corresponds to Lurie's scaled unstraightening equiva
Externí odkaz:
http://arxiv.org/abs/1910.06223
Publikováno v:
Int. Math. Res. Not. IMRN, rnz194, 2019
Inspired by work of Ladkani, we explain how to construct generalisations of the classical reflection functors of Bern\v{s}te\u{\i}n, Gel'fand and Ponomarev by means of the Grothendieck construction.
Comment: 8 pages; v2: minor edits
Comment: 8 pages; v2: minor edits
Externí odkaz:
http://arxiv.org/abs/1901.06993
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