Adjoint functors and equivalences of subcategories

Dualities and Equivalences Induced by Adjoint Functors

Adjoint Functors and Heteromorphisms

Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades, the notion of adjoint functors has moved to centerstage as category theory’s primary tool to characterize what is important in mathematics. Our focus here i...

Elementary Equivalences and Accessible Functors

We introduce the notion of λ-equivalence and λ-embeddings of objects in suitable categories. This notion specializes to L∞λ-equivalence and L∞λ-elementary embedding for categories of structures in a language of arity less than λ, and interacts well with functors and λ-directed colimits. We recover and extend results of Feferman and Eklof on “local functors” without fixing a language in advance....

Extension functors of generalized local cohomology modules and Serre subcategories

In this paper we present several results concerning the cofiniteness of generalized local cohomology modules.

Adjoint functors and tree duality

A family T of digraphs is a complete set of obstructions for a digraph H if for an arbitrary digraph G the existence of a homomorphism from G to H is equivalent to the non-existence of a homomorphism from any member of T to G. A digraph H is said to have tree duality if there exists a complete set of obstructions T consisting of orientations of trees. We show that if H has tree duality, then it...