On Gorenstein coalgebras

Abstract

We investigate the comodule representation category over the Morita-Takeuchi context coalgebra Γ and study the Gorensteinness of Γ. Moreover, we determine explicitly all Gorenstein injective comodules over the Morita-Takeuchi context coalgebra Γ and discuss the localization in Gorenstein coalgebras. In particular, we describe its Gabriel quiver and carry out some examples when the Morita-Takeuchi context coalgebra is basic.

Keywords

Gorenstein coalgebra / Gorenstein injective comodule / Gabriel quiver

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2016 Higher Education Press and Springer-Verlag Berlin Heidelberg