Definition Co-Optics [efr-G0YN]

Given \mathcal {M} acting on \mathcal {C}, \mathcal {D}, the category of co-optics, \mathsf {coOptic}_\mathcal {M}(\mathcal {C},\mathcal {D}) has objects pair {A \in \mathcal {D} \choose X \in \mathcal {C}}, and morphisms given by the coend \int ^M \mathcal {C}(X, M \cdot Y) \times \mathcal {D}(M \cdot A, B)