Tbilisi Mathematical Journal

Wobbly double functors

Robert Paré

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Abstract

We introduce a weakened notion of double functor, which we call wobbly, and which arises naturally in the study of double adjoints. We then show how horizontal invariance can be used to lift results about wobbly double functors to genuine ones.

Note

Dedicated to Marco Grandis on his seventieth birthday

Article information

Source
Tbilisi Math. J., Volume 8, Issue 1 (2015), 63-84.

Dates
Received: 22 August 2014
Accepted: 12 February 2015
First available in Project Euclid: 12 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768988

Digital Object Identifier
doi:10.1515/tmj-2015-0005

Mathematical Reviews number (MathSciNet)
MR3323915

Zentralblatt MATH identifier
1330.18007

Subjects
Primary: 18A30: Limits and colimits (products, sums, directed limits, pushouts, fiber products, equalizers, kernels, ends and coends, etc.)
Secondary: 18A25: Functor categories, comma categories

Keywords
Double functor double adjoint weak equivalence horizontal invariance

Citation

Paré, Robert. Wobbly double functors. Tbilisi Math. J. 8 (2015), no. 1, 63--84. doi:10.1515/tmj-2015-0005. https://projecteuclid.org/euclid.tbilisi/1528768988


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References

  • M. Grandis and R. Paré, Limits in double categories, Cahiers Topologie Géom. Différentielle Catég. 40, no. 3 (1999), p. 162-220.
  • M. Grandis and R. Paré, Adjoint for double categories, Cahiers Topologie Géom. Différentielle Catég. 45, no. 3 (2004), p. 193-240.
  • S. Lack, Notes on Paré's Theory of double categories, Private communication, Feb. 2014.