The Recollements of Abelian Categories: Cotorsion Dimensions and Cotorsion Triples

Localization and colocalization in tilting torsion theory for coalgebras

“…More importantly, Nȃstȃsescu and Torrecillas considered the colocalizing subcategory T , i.e., the functor T has a left adjoint H, instead of considering the localizing subcategory T , i.e., T is closed under arbitrary direct sums, or equivalently, T has a right adjoint S. Later, Navarro in [20] developed the ideas of Gabriel in the category of comodules by replacing the quotient category with a comodule category, which makes it easier to understand the localization for modules over an arbitrary algebra. The theory of localization for coalgebras has been developed by some scholars, see [8], [10], [11], [20], [21], [22], with the development of the representation theory of coalgebras, see [2], [5], [9], [12]- [18], [23]- [34], [39].…”