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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
2012/5/9
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...
Logical Construction of the Ionization Energy Theory and the Origin of Physical Categories
Logical Construction the Ionization Energy Theory the Origin of Physical Categories General Physics
2012/5/31
Logical proofs and definitions are developed to establish (i) the energy-level spacings, \xi for each chemical element (from the periodic table of chemical elements) can be converted to the ionization...
Traces in symmetric monoidal categories
Traces symmetric monoidal categories Category Theory
2011/9/29
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
2011/10/10
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...
Regard Renormalization in QED as Functor between Categories
Regard Renormalization QED Functor between Categories Mathematical Physics
2011/9/19
Abstract: To unify the quantum electrodynamics (QED) under the first principle which brings the renormalization unartificially, we study Feynman diagrams in QED according to the set theory and the cat...
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
2011/9/9
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
2011/8/25
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 ...