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Morita theory in enriched context

Kruna Segrt Ratkovic 1
1 Algebre Geometrie Topologie
JAD - Laboratoire Jean Alexandre Dieudonné
Abstract : We develop a homotopy theoretical version of classical Morita theory using the notion of a strong monad. It was Anders Kock who proved that a monad T in a monoidal category E is strong if and only if T is enriched in E. We prove that this correspondence between strength and enrichment follows from a 2-isomorphism of 2-categories. Under certain conditions on T, we prove that the category of T-algebras is Quillen equivalent to the category of modules over the endomorphism monoid of the T-algebra T (I) freely generated by the unit I of E . In the special case where E is the category of Γ-spaces equipped with Bous field-Friedlander's stable model structure and T is the strong monad associated to a well-pointed Γ-theory, we recover a theorem of Stefan Schwede, as an instance of a general homotopical Morita theorem.
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Submitted on : Tuesday, February 5, 2013 - 6:31:14 PM
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Kruna Segrt Ratkovic. Morita theory in enriched context. Category Theory [math.CT]. Université Nice Sophia Antipolis, 2012. English. ⟨tel-00785301⟩

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