Tbilisi Mathematical Journal

Wobbly double functors

Robert Paré

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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.


Dedicated to Marco Grandis on his seventieth birthday

Article information

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Double functor double adjoint weak equivalence horizontal invariance


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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  • 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.