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Derived equivalences induced by big cotilting modules

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arxiv 1308.1804 v2 pith:IKGY6AQT submitted 2013-08-08 math.CT math.RAmath.RT

Jan Stovicek This is my paper · ORCID
classification math.CTmath.RAmath.RT
keywords equivalencecotiltinginducedmoduleprovetriangleabelianbase
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We prove that given a Grothendieck category G with a tilting object of finite projective dimension, the induced triangle equivalence sends an injective cogenerator of G to a big cotilting module. Moreover, every big cotilting module can be constructed like that in an essentially unique way. We also prove that the triangle equivalence is at the base of an equivalence of derivators, which in turn is induced by a Quillen equivalence with respect to suitable abelian model structures on the corresponding categories of complexes.

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  1. Coderived and contraderived categories for a cotorsion pair, flat-type cotorsion pairs, and relative periodicity

    math.CT 2025-09 conditional novelty 7.0 of 10

    For hereditary complete cotorsion pairs generated by a set in a Grothendieck category, the coderived category of the left class is equivalent to the contraderived category of the right class, and for sandwiched pairs ...

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