Non-exact Integral Functors

TL;DR

This paper introduces a generalized concept of integral functors in k-linear and graded categories, demonstrating that all such functors can be viewed as integral in this broader framework.

Contribution

It extends the notion of integral functors to a non-exact setting within k-linear and graded categories, proving all such functors are integral.

Findings

Every k-linear and graded functor is integral in the new framework.

The notion of non-exact integral functors broadens the applicability of integral functor theory.

Abstract

We give a natural notion of (non-exact) integral functor in the context of k-linear and graded categories. In this broader sense, we prove that every k-linear and graded functor is integral.