Related papers: Basic Bicategories

An expository hitchhikers guide to some theorems in mathematics.

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…

Interest in weak cubical n-categories arises in various contexts, in particular in topological field theories. In this paper, we describe a concept of double bicategory, namely a strict model of the theory of bicategories in Bicat. We show…

The basic notions related to coherence phenomena are formulated. Two types of coherence are described, state coherence and transition coherence. Useful characteristics for quantifying coherence are defined, such as coherence functions,…

This article gives an elementary and formal 2-categorical construction of a bicategory of right fractions analogous to anafunctors, starting from a 2-category equipped with a family of covering maps that are fully faithful and co-fully…

In this thesis I lift the Curry--Howard--Lambek correspondence between the simply-typed lambda calculus and cartesian closed categories to the bicategorical setting, then use the resulting type theory to prove a coherence result for…

The category of matchings between finite sets extends to the category of cobordisms of signed sets. A chain of cobordisms that starts and ends with unsigned sets A and B yields a matching from A to B. This is a convenient way to package the…

For a collection of subcategories satisfying a fixed set of conditions, for example thick subcategories of a triangulated category, we define a topological space called classifying space of subcategories. We show that this space classifies…

General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.

This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…

Proofs of coherence in category theory, starting from Mac Lane's original proof of coherence for monoidal categories, are sometimes based on confluence techniques analogous to what one finds in the lambda calculus, or in term-rewriting…

In this paper we introduce the theory of ends and coends in the context of enriched bicategories. This will be an enriched version of the theory introduced in [Cor16], and a bicategorical version of the classical theory of enriched…

We prove a coherence theorem for braided monoidal bicategories and relate it to the coherence theorem for monoidal bicategories. We show how coherence for these structures can be interpretted topologically using up-to-homotopy operad…

We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.

We introduce the bicategory of bialgebras with coverings (which can be thought of as coalgebra-indexed families of morphisms), and provide a motivating application to the transfer of formulas for primitives and antipode. Additionally, we…

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…

This paper proves three different coherence theorems for symmetric monoidal bicategories. First, we show that in a free symmetric monoidal bicategory every diagram of 2-cells commutes. Second, we show that this implies that the free…

Categories of W*-bimodules are shown in an explicit and algebraic way to constitute an involutive W*-bicategory.

We describe some of the basic properties of the 2-category of 2-term complexes in an abelian category, using butterflies as morphisms.