On the negative-one shift functor for FI-modules

We show that the negative-one shift functor S˜−1 on the category of FI-modules is a left adjoint of the shift functor S and a right adjoint of the derivative functor D. We show that for any FI-module V, the coinduction QV of V is an extension of V by S˜−1V.

Saved in:
Bibliographic Details
Published in:Journal of pure and applied algebra 2017-05, Vol.221 (5), p.1242-1248
Main Author: Gan, Wee Liang
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We show that the negative-one shift functor S˜−1 on the category of FI-modules is a left adjoint of the shift functor S and a right adjoint of the derivative functor D. We show that for any FI-module V, the coinduction QV of V is an extension of V by S˜−1V.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2016.09.010