nLab internal pseudocategory

Idea

The notion of an internal pseudocategory in a 2-category $K$ with pullbacks is a generalisation of the notion of an internal category in a 1-category, where one requires composition to be associative and unital only up to coherent isomorphism of 2-cells in $K$.

This is distinct from the concept of an internal bicategory?, which additionally specifies the data of an object of 2-cells.

Examples

• A pseudo double category is pseudocategory internal to the 2-category Cat (while a strict double category is a category internal to the underlying 1-category of Cat).

Related concepts

• internalization

• internal category in an $(\infty,1)$-category

References

• N. Martins-Ferreira. Pseudo-categories Journal of Homotopy and Related Structures 1.1 (2006): 47-78. (arXiv:math/0604549)