Comodules, contramodules and Pontryagin duality

John MacQuarrie; Ricardo Souza

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arXiv · 1806.03714

Comodules, contramodules and Pontryagin duality

John MacQuarrie·Ricardo Souza

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Abstract

Let $C$ be a $k$-coalgebra, where $k$ is a field. The category of pseudocompact left $C^*$-modules is dual to both the category of discrete right $C^*$-modules and to the category of left $C$-comodules. We obtain this way two sides of a square of dualities. In this note we complete the square by introducing as fourth corner the category of pseudocompact right $C$-contramodules. We use these dualities to extend a natural isomorphism of Takeuchi.

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BibTeX RIS

John MacQuarrie, Ricardo Souza. 2018-06-10. Comodules, contramodules and Pontryagin duality. https://arxiv.org/abs/1806.03714

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