The Hidden Strength of Costrong Functors

Strong functors and monads are ubiquitous in Computer Science. More recently, comonads have demonstrated their use in structuring context-dependent notions of computation. However, the dualisation of ``being strong'' property passed somehow unobserved so far. We argue that ``being costrong'' gives a different understanding of how functors can interact with monoidal structures. This work in progress aims to explore costrong functors and their natural properties, with an eye towards the semantics of computations.