nLab monad retromorphism

Idea

A retromorphism of monads is a retrocell between the carriers of the monads, which preserves the unit and multiplication.

Examples

• A monad internal to the double category $Span$ is a small category. A monad retromorphism is then a retrofunctor.

References

The terminology is introduced in the following thesis, where the definition is alluded to:

• Matthew Di Meglio, The category of asymmetric lenses and its proxy pullbacks. Master’s thesis. Macquarie University, 2021. doi: 10.25949/20236449, pdf

A definition is introduced in:

• Bryce Clarke, The double category of lenses, PhD thesis, Macquarie University, 2022. (doi:10.25949/22045073.v1)

Monad retromorphisms are further studied in:

• Robert Paré, Retrocells, arXiv:2306.06436