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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Non-abelian Derived Categories and Derived Schur and Weyl Functors
非阿贝尔派生范畴 派生舒尔 外尔函子
2023/4/13
We'll start with reviewing Quillen and Lurie's theory of non-abelian derived categories (also known as the "animation" theory). Following that, we will apply this theory to generalize the classical Sc...
Options of traveling to Nankai University NOTE: On Sept 4, CIM will organize 3 buses to Beijing airport to pick up the participants (morning, noon and evening). Once you book your flight, please let...
Let S be a monoidal category with equalizers that are preserved by the tensor
product. The notion of categories internal to S is defined, generalizing the notions
of monoid and comonoid in S, and ex...
Open-string vertex algebras, tensor categories and operads
Open-string vertex algebras tensor categories operads
2015/3/25
We introduce notions of open-string vertex algebra, conformal open-string vertex algebra and variants of these notions. These are ``open-string-theoretic,'' ``noncommutative'' generalizations of the n...
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, qua...
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 s...
Skew monoidales, skew warpings and quantum categories
bialgebroid fusion operator quantum category monoidal bicategory monoidale skew-monoidal category
2012/5/1
Kornel Szlach\'anyi recently used the term skew-monoidal category for a particular laxified version of monoidal category. He showed that bialgebroids $H$ with base ring $R$ could be characterized in t...
Traces in symmetric monoidal categories
Traces symmetric monoidal categories Category Theory
2011/7/29
Abstract: The purpose of this expository note is to describe duality and trace in a symmetric monoidal category, along with important properties (including naturality and functoriality), and to give a...
Causal categories: relativistically interacting processes
Causal categories General Relativity and Quantum Cosmology Category Theory
2011/7/29
Abstract: A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This stru...
Abstract: This paper deals with questions relating to Haghverdi and Scott's notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every ...
Abstract: In this paper we introduce the definition of partial action on small $k$-categories generalizing the similar well known notion of partial actions on algebras. The point of view of partial ac...
Derived equivalences in n-angulated categories
derived equivalence n-angulated category n-perforated Yoneda algebra triangulated category
2011/7/15
Abstract: In this paper, we consider $n$-perforated Yoneda algebras for $n$-angulated categories, and show that, under some conditions, $n$-angles induce derived equivalences between the quotient alge...
A geometric interpretation of the triangulated structure of m-cluster categories
m-cluster categories triangulated structure Auslander-Reiten triangles orbit categories Auslander Reiten quivers
2011/7/6
Abstract: The aim of this note is to answer several open problems arising from the geometric description of the $m$-cluster categories of type $A_n$ and their realization in terms of the $m$-th power ...
Homotopy categories and idempotent completeness, weight structures and weight complex functors
Homotopy category idempotent completeness weight structure w-structure weight complex functor
2011/7/6
Abstract: This article provides some basic results on weight structures, weight complex functors and homotopy categories. We prove that the full subcategories K(A)^{w < n}, K(A)^{w > n}, K(A)^- and K(...
Stratifications of derived categories from tilting modules over tame hereditary algebras
Adele ring Recollement Stratification Tame hereditary algebra Tilting module Universal localization
2011/7/3
Abstract: n this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form $R_{\mathcal U}\oplus R_{\mathcal U}/R$ over tame hereditary $k$-algebras $R$ with $k$...