The adjoint cotranspose of modules with respect to subcategories
Volume 163 / 2021
Colloquium Mathematicum 163 (2021), 23-36
MSC: Primary 18G25; Secondary 16E30.
DOI: 10.4064/cm7900-9-2019
Published online: 25 May 2020
Abstract
Let $\mathcal X $ be a subcategory of left $S$-modules and $_{R}U_{S}$ an $(R, S)$-bimodule. As a generalization of an adjoint cotranspose, we introduce an adjoint $\mathcal X $-cotranspose of a left $S$-module relative to $_{R}U_{S}$ and study its homological properties. Let $\mathcal V $ be a subcategory of $\mathcal X $. The relations between adjoint $\mathcal X $-cotransposes and adjoint $\mathcal V $-cotransposes are investigated under the condition that $\mathcal V $ is a generator or cogenerator for $\mathcal X $. Then we give some applications of these results to some categories of interest. In particular, the adjoint counterparts of Gorenstein cotransposes are established.
