In 2013, Krause defined a new product of strict polynomial functors, with various applications including a new construction of Ringel and Serre duality for the category of strict polynomial functors.
The category of strict polynomial functors is equivalent to a limit of categories of polynomial representations of general linear groups. Such categories have been studied enormously, beginning with the work of Schur in 1901. Still it was not obvious without the tools of category theory that such a product should exist for polynomial representations of the general linear group.
In this talk we give a new construction of Krause's product using only the classical theory of polynomial representations of general linear groups i.e. only using tools available to Schur in 1901. We will outline the anachronistic derivation of this construction from Krause's product.