On the negative-one shift functor for FI-modules
Wee Liang Gan
TL;DR
This paper explores the properties of the negative-one shift functor in FI-modules, establishing its adjoint relationships with the shift and derivative functors, and clarifying its connection to the coinduction functor.
Contribution
It provides a detailed analysis of the negative-one shift functor, revealing its adjoint relationships and its link to the coinduction functor within FI-modules.
Findings
Negative-one shift functor is a left adjoint of the shift functor.
Negative-one shift functor is a right adjoint of the derivative functor.
The coinduction functor is related to the negative-one shift functor.
Abstract
We show that the negative-one shift functor on the category of FI-modules is a left adjoint of the shift functor and a right adjoint of the derivative functor. We also describe how the coinduction functor is related to the negative-one shift functor.
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