Monoidal Morita equivalence
type: Item
instance of: scholarly article
title: Monoidal Morita equivalence
zbMATH Open document ID: 0693.18005
DOI: 10.1016/0022-4049(89)90132-1
author: S. R. Johnson
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: Morita equivalence has been studied for categories enriched over a monoidal category. The author considers enriched categories possessing themselves a monoidal structure and derive many of the Morita theorems in this context. The key used is the definition of a monoidal Cauchy completion. Im and Kelly have studied the free monoidal cocompletion of a small enriched category. Much of their work extends to free monoidal \b{F}-cocompletions where \b{F} is any set of weights for colimits. One has also to use an observation of R. Street that the Cauchy completion is just the free cocompletion under absolute colimits, to enrich the monoidal structure on the Cauchy completion of any small monoidal category. Finally, conditions under which the monoidal Cauchy completion is closed are also discussed.
reviewed by: Grigore Călugăreanu
Mathematics Subject Classification ID: 18D20
zbMATH DE Number: 4134283
zbMATH Keywords: accessible functors
zbMATH Keywords: separately cocontinuous functors
zbMATH Keywords: strong monoidal functor
zbMATH Keywords: near adjoint
zbMATH Keywords: near closed
zbMATH Keywords: enriched categories with monoidal structure
zbMATH Keywords: Morita equivalence
zbMATH Keywords: monoidal Cauchy completion
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90132-1
OpenAlex ID: W2054640438
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description: scientific article; zbMATH DE number 4134283