相关论文: Category Theory in Coq 8.5

In this paper, we introduce a new type of $ pq $-calculus. The $ pq $-derivative and $ pq $-integration are investigated and various properties of these concepts are given. The fundamental theorem of $ pq $-calculus and formulas of $ pq…

Category theory provides an alternative to Hilbert's Formal Axiomatic method and goes beyond Mathematical Structuralism

We review several known categorification procedures, and introduce a functorial categorification of group extensions with applications to non-abelian group cohomology. Categorification of acyclic models and of topological spaces are briefly…

Category Theory is a well-known powerful mathematical modeling language with a wide area of applications in mathematics and computer science, including especially the semantical foundations of topics in software science and development.…

We introduce a notion of globular multicategory with homomorphism types. These structures arise when organizing collections of "higher category-like" objects such as type theories with identity types. We show how these globular…

With the development of topological field theory, the mathematical tool of the tensor category was also introduced into physics. Traditional group theory corresponds to a special category,group category. Tensor categories can describe…

Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…

This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to…

In this paper we introduce the models for $(\infty, n)$-categories which have been developed to date, as well as the comparisons between them that are known and conjectured. We review the role of $(\infty, n)$-categories in the proof of the…

We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…

Initial Semantics aims at characterizing the syntax associated to a signature as the initial object of some category. We present an initial semantics result for typed higher-order syntax together with its formalization in the Coq proof…

We define natural A_infinity-transformations and construct A_infinity-category of A_infinity-functors. The notion of non-strict units in an A_infinity-category is introduced. The 2-category of (unital) A_infinity-categories, (unital)…

The question "What is category theory" is approached by focusing on universal mapping properties and adjoint functors. Category theory organizes mathematics using morphisms that transmit structure and determination. Structures of…

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would…

We study a metric-like structure on categories, showing that the concept of the limit of a sequence in a metric space and the concept of the colimit of a sequence in a category have a common generalization. The main concept is a norm on a…

We introduce a new approach to the study of operational theories of physics using category theory. We define a generalisation of the (causal) operational-probabilistic theories of Chiribella et al. and establish their correspondence with…

We adapt the classical framework of algebraic theories to work in the setting of (infinity,1)-categories developed by Joyal and Lurie. This gives a suitable approach for describing highly structured objects from homotopy theory. A central…

In this review we report on how the problem of general covariance is treated within the algebraic approach to quantum field theory by use of concepts from category theory. Some new results on net cohomology and superselection structure…

We construct an algebraic-cycle based model for the motivic cohomology on the category of schemes of finite type over a field, where schemes may admit arbitrary singularities and may be non-reduced. We show that our theory is functorial on…

In this paper we redevelop the foundations of the category theory of quasi-categories (also called infinity-categories) using 2-category theory. We show that Joyal's strict 2-category of quasi-categories admits certain weak 2-limits, among…