collage of an adjunction

• up monad and down comonad of an adjunction collage
• two compositions on an adjunction collage
• failure of associativity on an adjunction collage

Notes.

• This is a particular case of the collage of a profunctor, where the profunctor is that associated to the adjunction: either the representable profunctor on the right adjoint, or the corepresentable profunctor on the left adjoint.

References.

• Classical notions of computation and the Hasegawa-Thielecke theorem (Mangel, Melliès, Munch-Maccagnoni, 2025)

Tags: adjunction.