  We further the theory of optics or "circuits-with-holes" to encompass
premonoidal categories: monoidal categories without the interchange law. Every
premonoidal category gives rise to an effectful category (i.e. a generalised
Freyd-category) given by the embedding of the monoidal subcategory of central
morphisms. We introduce "pro-effectful" categories and show that optics for
premonoidal categories exhibit this structure. Pro-effectful categories are the
non-representable versions of effectful categories, akin to the generalisation
of monoidal to promonoidal categories. We extend a classical result of Day to
this setting, showing an equivalence between pro-effectful structures on a
category and effectful structures on its free tight cocompletion. We also
demonstrate that pro-effectful categories are equivalent to prostrong
promonads.
