Tilting theory - an introduction
Topological Hochschild cohomology and generalized Morita equivalence.
Topological linear compactness for Grothendieck categories. Theorem of Tychonoff. Applications to coalgebras.
We show the Tychonoff's theorem for a Grothendieck category with a set of small projective generators. Strictly quasi-finite objects for semiartinian Grothendieck categories are characterized. We apply these results to the study of the Morita duality of dual algebra of a coalgebra.
Torsion free types
Trisections of module categories
Let A be a finite-dimensional algebra over a field k. We discuss the existence of trisections (mod₊ A,mod₀ A,mod₋ A) of the category of finitely generated modules mod A satisfying exactness, standardness, separation and adjustment conditions. Many important classes of algebras admit trisections. We describe a construction of algebras admitting a trisection of their module categories and, in special cases, we describe the structure of the components of the Auslander-Reiten quiver lying in mod₀ A.
Tubular mutations
Twisted Hopf Algebras.