… generated t-structures (in any ambient triangulated category with coproducts), we prove
that the heart is a locally finitely presented Grothendieck category. We use functor categories …

… We study t-structures with Grothendieck hearts on compactly … categories \({\mathcal {T}}\)
that are underlying categories of … two kinds of smashing t-structure with Grothendieck hearts: …

… triangulated category, then the heart of … heart of any compactly generated t-structure of a
well-generated algebraic or topological triangulated category is a Grothendieck Abelian category…

… when the heart of a t-structure is a Grothendieck category, … in the derived category of a
Grothendieck category associated to … information on the HRS t-structures which have a projective …

… , which includes, in the case of the derived category of a Grothendieck category, a large
class of t-structures whose hearts have at most n fixed consecutive non-zero cohomologies. …

… all compactly generated t-structures in D(R) … heart which is a Grothendieck category.
Moreover, we identify all compactly generated t-structures in D(R) whose heart is a module category…

… Nowadays, t-structures are used in several branches of … has a heart which is a Grothendieck
category with good … (unbounded) derived category D(G) of a Grothendieck category G which …

… First, we give the definition and properties of a Grothendieck category. Passing … category
and define t-structures. Afterwards, we focus our attention on purity in Grothendieck categories, …

… of an arbitrary Grothendieck category equipped with a TTF triple. In view of this result, a large
part of the chapter is focused in specialising it to the hearts of the t-structures of our interest, …

… when the heart of some classes of t-structures is … heart is a Grothendieck category in terms
of the properties of S-modules. In particular, we show that the heart is a Grothendieck category …