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Israel Journal of Mathematics

, Volume 227, Issue 1, pp 239–287 | Cite as

Homotopical Morita theory for corings

  • Alexander Berglund
  • Kathryn HessEmail author
Article
  • 36 Downloads

Abstract

A coring (A,C) consists of an algebra A in a symmetric monoidal category and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf–Galois extensions and descent theory, as well as in the study of Hopf algebroids. In this paper, we address the question of when two corings (A,C) and (B,D) in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules V A C and V B D are Quillen equivalent. As an illustration of the general theory, we examine homotopical Morita theory for corings in the category of chain complexes over a commutative ring.

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Copyright information

© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Department of MathematicsStockholm UniversityStockholmSweden
  2. 2.SV BMI UPHESSÉcole Polytechnique Fédérale de LausanneLausanneSwitzerland

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