Dear Jonathon, A definition of 2-fibration is given in the following sources:Claudio Hermida, "Some properties of Fib as a fibered 2-category", J. Pure Appl. Alg. 134-1 (1999) 83-109.Claudio Hermida, "Descebt on 2-fibrations and strongly 2-regular 2-categories", App. Cat. Str. 12 (2004) 427--459. It is adopted (Definition 4.1) and used in Marta Bunge and Claudio Hermida, 'Pseudomonadicity and 2-stack completions", Proceedings of the MakkaiFest, CRM Proceedings and Lecture Notes, to appear 2011, a preprint of which I shall send to anyone requesting it. Best wishes,Marta Bunge ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill UniversityBurnside Hall, Office 1005 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 Office: (514) 398-3810/3800 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/~bunge/ ************************************************
To: categories@mta.ca From: chichejonathan@gmail.com Subject: categories: Adjunctions and fibrations in 2-Cat Date: Mon, 28 Feb 2011 12:15:27 +0100
Dear all,
Is the notion of adjunction in 2-Cat well-understood? Here, 2-Cat stands for a 3-category the objects of which are 2-categories. I am mainly interested in the case where everything is strict, but comments on the non-strict cases are welcome.
There has been a discussion recently about what should be the definition of fibration in an arbitrary 2-category. I do not expect the notion to be defined for general 3-categories, but is there at least a definition for the notion of fibration in 2-Cat?
Many thanks in advance for your help!
Jonathan Chiche
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]