Reducts of functors

A reduced functor between pointed categories is one that preserves the zero object. A multi-variable functor is reduced if it preserves the zero object in each variable separately. Given a (not-necessarily reduced) multi-variable functor, we can take its associated reduced functor, which we call it's reduct. The co-smash product, discussed in the previous talk, is the reduct of the coproduct (multi-variable) functor. We will explain these observations, along with a few applications and generalizations.

The talk is based on joint work with Corentin Vienne and Tim Van der Linden.