Poincar\'e duality for Ext-groups between strict polynomial fucnctors

TL;DR

This paper explores dualities in Ext-groups within the category of strict polynomial functors by examining the relationship between adjoint functors to precomposition.

Contribution

It establishes new dualities in Ext-groups by analyzing the interplay between left and right adjoint functors in strict polynomial functor categories.

Findings

Derived dualities in Ext-groups

Connected adjoint functors to precomposition

Enhanced understanding of polynomial functor categories

Abstract

We study relation between left and right adjoint functors to the precomposition functor. As a cosnequence we obtain various dualities in the Ext-groups in the category of strict polynomial functors.