Adjunctions and fibrations in 2-Cat

Adjunctions and fibrations in 2-Cat

[Jonathan CHICHE 齊正航]

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


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RE: Adjunctions and fibrations in 2-Cat

[Marta Bunge]

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/ ]