Related papers: Category of A_infinity-categories

We introduce the category of finite strings and study its basic properties. The category is closely related to the augmented simplex category, and it models categories of linear representations. Each lattice of non-crossing partitions…

We define A-infinity-bimodules similarly to Tradler and show that this notion is equivalent to an A-infinity-functor with two arguments which takes values in the differential graded category of complexes of k-modules, where k is a ground…

We give a natural notion of (non-exact) integral functor in the context of k-linear and graded categories. In this broader sense, we prove that every k-linear and graded functor is integral.

This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…

We give two examples of categorical axioms asserting that a canonically defined natural transformation is invertible where the invertibility of any natural transformation implies that the canonical one is invertible. The first example is…

We define the notion of an indexed profunctor over a 2-category, and use it to develop an abstract theory of limits. The theory subsumes (conical) limits, weighted limits, ends and Kan extensions. Results include an abstract version of the…

A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…

We provide a complete description of the category of pseudo-categories (including pseudo-functors, natural and pseudo-natural transformations and pseudo modifications). A pseudo-category is a non strict version of an internal category. It…

The aim of this paper is twofold. One is to give a definition of the Euler characteristic of infinite acyclic categories with filtrations and the other is to prove the invariance of the Euler characteristic under the subdivision of finite…

This note is a contribution written for the second volume of the Encyclopedia of mathematical physics. We give an informal introduction to the notions of an $(\infty,n)$-category and $(\infty,n)$-functor, discussing some of the different…

Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set…

We propose a definition of higher inductive types in $(\infty,1)$-categories with finite limits. We show that the $(\infty,1)$-category of $(\infty,1)$-categories with higher inductive types is finitarily presentable. In particular, the…

The categories with noninvertible morphisms are studied analogously to the semisupermanifolds with noninvertible transition functions. The concepts of regular n-cycles, obstruction and the regularization procedure are introduced and…

Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general…

We give an introduction to constructive category theory by answering two guiding computational questions. The first question is: how do we compute the set of all natural transformations between two finitely presented functors like…

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…

We want to replace categories, functors and natural transformations by categories, open functors and open natural transformations. In analogy with open dynamical systems, the adjective open is added here to mean that some external…

We suggest two approaches to a definition of unitarity for pseudonatural transformations between unitary pseudofunctors on pivotal dagger 2-categories. The first is to require that the 2-morphism components of the transformation be unitary.…

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…