Equivalences in Bicategories
author
Abstract:
In this paper, we establish some connections between the concept of an equivalence of categories and that of an equivalence in a bicategory. Its main result builds upon the observation that two closely related concepts, which could both play the role of an equivalence in a bicategory, turn out not to coincide. Two counterexamples are provided for that goal, and detailed proofs are given. In particular, all calculations done in a bicategory are fully explicit, in order to overcome the difficulties which arise when working with bicategories instead of 2-categories.
similar resources
Basic Bicategories
A concise guide to very basic bicategory theory, from the definition of a bicategory to the coherence theorem.
full textMonads and Interpolads in Bicategories
Given a bicategory, Y , with stable local coequalizers, we construct a bicategory of monads Y -mnd by using lax functors from the generic 0-cell, 1-cell and 2-cell, respectively, into Y . Any lax functor into Y factors through Y -mnd and the 1-cells turn out to be the familiar bimodules. The locally ordered bicategory rel and its bicategory of monads both fail to be Cauchy-complete, but have a ...
full textIntroduction to linear bicategories
Linear bicategories are a generalization of bicategories, in which the one horizontal composition is replaced by two (linked) horizontal compositions. These compositions provide a semantic model for the tensor and par of linear logic: in particular, as composition is fundamentally noncommutative, they provide a suggestive source of models for noncommutative linear logic. In a linear bicategory,...
full textWide Morita Contexts in Bicategories
We give a formal concept of (right) wide Morita context between two 0-cells in arbitrary bicategory. We then construct a new bicategory with the same 0-cells as the oldest one, and with 1-cells all these (right) wide Morita contexts. An application to the (right) Eilenberg-Moore bicategory of comonads associated to the bimodules bicategory is also given.
full textBicategories of Concurrent Games
This paper summarises recent results on bicategories of concurrent games and strategies. Nondeterministic concurrent strategies, those nondeterministic plays of a game left essentially unchanged by composition with copy-cat strategies, have recently been characterized as certain maps of event structures. This leads to a bicategory of general concurrent games in which the maps are nondeterminist...
full textFunctorial Calculus in Monoidal Bicategories
The definition and calculus of extraordinary natural transformations [EK] is extended to a context internal to any autonomous monoidal bicategory [DyS]. The original calculus is recaptured from the geometry [SV], [MT] of the monoidal bicategory V-Mod whose objects are categories enriched in a cocomplete symmetric monoidal category V and whose morphisms are modules. Mathematics Subject Classific...
full textMy Resources
Journal title
volume 8 issue 1
pages 19- 33
publication date 2018-01-01
By following a journal you will be notified via email when a new issue of this journal is published.
Keywords
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023