Pseudo pure-injective objects

Pure-injective modules

The pure-injective R-modules are defined easily enough: as those modules which are injective over all pure embeddings, where an embedding A → B is said to be pure if every finite system of R-linear equations with constants from A and a solution in B has a solution in A. But the definition itself gives no indication of the rich theory around purity and pure-injectivity. The purpose of this surve...

Superdecomposable pure-injective modules

Existence of superdecomposable pure-injective modules reflects complexity in the category of finite-dimensional representations. We describe the relation in terms of pointed modules. We present methods for producing superdecomposable pure-injectives and give some details of recent work of Harland doing this in the context of tubular algebras. 2010 Mathematics Subject Classification. Primary 16G...

Injective objects in triangulated categories

Type-checking injective pure type systems

Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(?jM) and sort(?jM), where ? is a pseudo-context and M is a pseudo-term, and such that for every sort s, ? ` M : A ^ ? ` A : s) elmt(?jM) = s ? ` M : s) sort(?jM) = s By eliminating the problematic clause in the (abstraction) rule in favour of constraints over el...

Order-adjoint monads and injective objects

Given a monad T on Set whose functor factors through the category of ordered sets with left adjoint maps, the category of Kleisli monoids is defined as the category of monoids in the hom-sets of the Kleisli category of T. The Eilenberg-Moore category of T is shown to be strictly monadic over the category of Kleisli monoids. If the Kleisli category of T moreover forms an order-enriched category,...