… 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 …

… 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 …

… 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 …

… 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 …

… on triangulated categories, but also on exact categories. In … categories which are neither
exact nor triangulated (see [16… tilting theory in extriangulated categories and τ-tilting theory. In …

… We discuss tilting objects in exact categories. An object 𝑇 of an exact category A is a tilting
… There is an analogous notion of a tilting object in a triangulated category and we see that 𝑇 …

… One of the fundamental consequences of Tilting Theory, … the so-called Morita theory for
derived categories. Indeed, Happel [… category [42], where the conflations are given by short exact …

… tilting subcategory. We show that \({\mathcal {C}}\) is cluster tilting if and only if the factor
category \({\… the related results on a triangulated category and is new for an exact category case. …

… categories and their induced exact equivalences, alongside with a Cap [GSP22] and
homalg [hom22] based implementation of this framework in the computer algebra system GAP […

… categories. In this thesis we focus on two particular theories, whose origins can be traced
back to tilting theory. … using Bongartz’s exact sequence for partial tilting modules that for an …