2018/06/10 by John MacQuarrie, MacQuarrie, John, Ricardo Lehtonen Rodrigues de Souza +1
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Commutative Algebra and Its Applications
paper · pdf · doi:10.48550/arxiv.1806.03714
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.