Cotilting modules are pure-injective

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Direct limits in the heart of a t-structure: The case of a torsion pair☆ (2013, background): “morphism F′ ։U, for some F′ ∈F. But, by the dual of proposition 5.2, we get that each injective cogenerator E is an homomorphic image of an object in F= Cogen(Q). 2) We follow Bazzoni’s argument (see [B]) and see that it also works in our context. First of all, note that an object Y of Gis pure-inje”
Tilting modules and Gorenstein rings (2006, background): “By [ 11 ], C is pure-injective, so C is a direct summand in C⁄⁄,”
One Dimensional Tilting Modules are of Finite Type (2008, result): “The following result is dual to the result (proved in [ 7 ]) stating that cotilting torsion free classes are closed under direct limits, hence definable.”
Torsion pairs in silting theory (2016, background): “Note that, since C is pure-injective in Mod(A) by [7], it follows from Theorem 3.”
Tilting, cotilting, and spectra of commutative noetherian rings (2012, background): “5], since all 1-cotilting modules are pureinjective by [4].”
Cosilting Modules (2015, methodology): “We have the following construction given by Bazzoni in the proof of [7, Proposition 2.5].”