FP-Cosilting and FP-Cotilting Modules

We introduce the concepts of FP-cosilting and FP-cotilting modules, which extend finitely cosilting modules and finitely cotilting modules (Colby-modules) from the ∏\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\prod $$\end{document}-coherent case to the coherent case. Some properties of FP-cosilting and FP-cotilting modules, including a Cotilting Theorem induced by these modules, are obtained.