In this work we define a 2-dimensional analogue of extranatural transformation and use these to characterise codescent objects. They will be seen as universal objects amongst pseudo-extranatural transformations in a similar manner in which coends are universal objects amongst extranatural transformations. Some composition lemmas concerning these transformations are introduced and a Fubini theorem for codescent objects is proven using the universal characterisation description.
Keywords: Codescent object, pseudo-extranatural, Fubini
2010 MSC: 18D05, 18D10
Theory and Applications of Categories, Vol. 34, 2019, No. 24, pp 684-713.