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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...
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...
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 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...
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...
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: 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...
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...
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 ...

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