An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...

We study 2-monads and their algebras using a Cat-enriched version of Quillen model categories, emphasizing the parallels between the homotopical and 2-categorical points of view. Every 2-category with finite limits and colimits has a canonical model structure in which the weak equivalences are the equivalences; we use these to construct more interesting model structures on 2-categories, includi...

Let T be the functor on the category of unstable algebras over the Steenrod algebra constructed by Lannes. We use an argument involving Kähler differentials to show that T preserves polynomial algebras. This leads to new and relatively simple proofs of some topological and algebraic theorems. §

For a symmetric monoidal-closed category V and a suitable monad T on the category of sets, we introduce the notion of reflexive and transitive (T,V)-algebra and show that various old and new structures are instances of such algebras. Lawvere’s presentation of a metric space as a V-category is included in our setting, via the Betti-Carboni-Street-Walters interpretation of a V-category as a monad...

We introduce the concept of pseudotwistor (with particular cases called twistor and braided twistor) for an algebra (A,μ, u) in a monoidal category, as a morphism T : A⊗ A → A ⊗ A satisfying a list of axioms ensuring that (A,μ ◦ T, u) is also an algebra in the category. This concept provides a unifying framework for various deformed (or twisted) algebras from the literature, such as twisted ten...

In this paper we argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. T...