… We define tilting subcategories in arbitrary exact categories to archieve the following. Firstly:
… of tilting subcategories to arbitrary exact categories. Discuss standard results for tilting …

… a theory of big tilting and cotilting objects of possibly infinite homological dimension in abelian
categories. … Finally, in the role of our abelian category B, Enomoto has an exact category …

… We will provide maps(c) with a structure of exact category such that, tilting subcategories
of mod(c) will correspond to relative tilting subcategories of maps(c). We begin the section …

… tilting theory to arbitrary functor categories, having in mind applications to the functor category
… the functor C(Ti, ) to the above exact sequence to obtain by the long exact sequence an …

… By applying HomZ( ,Q/Z) to the bottom sequence and by comparing it with the exact sequence
above we obtain the desired isomorphism. To prove the naturality of the isomorphism we …

… In this article we show that all kinds of tilting arise from a special class of exact categories (in
… we call tilting categories. For an n-tilting module [Citation4, Citation12], the associated tilting …

… that can be embedded nicely in an abelian category. In particular, we will show … tilting
theory in exact categories built this way, coincides with tilting objects in extriangulated categories …

… exact adjoint functors between two abelian categories induces a pair of adjoint functors
between their derived categories… This generalizes an idea first used in tilting theory by Vossieck […

… exact categories is fundamental in the representation theory of algebras, such as the tilting
theory in derived categories … kinds of exact categories as U ⊥ among all exact categories by …

… Inspired by them, we introduce the notion of tilting category in order to give a unified approach
of … The main property that we will use is the existence of the exact sequences given by the …