In categorical universal algebra, it is well known that a finitary equational presentation of algebras in a finitary variety K amounts to the existence of a coequaliser of a pair of morphisms between finitely generated free algebras. The essence of a universal-algebraic flavour of a finitary functor L : K −→ K is that L is determined by its behaviour on finitely generated free algebras. In fact...

Let R be a commutative noetherian ring. We study the behavior of injectiveand at dimension of R-modules under the functors HomR(-,-) and -×R-.

We study the transfer of (dual) relative CS-Rickart properties via functors between abelian categories. consider fully faithful as well adjoint pairs functors. give several applications to Grothendieck categories and, in particular, (graded) module and comodule

The Structural Induction Theorem (Lehmann and Smyth, 1981; Plotkin, 1981) characterizes initial F-algebras of locally continuous functors F on the category of cpo's with strict and continuous maps. Here a dual of that theorem is presented, giving a number of equivalent characterizations of nal coalgebras of such functors. In particular, nal coalgebras are order strongly-extensional (sometimes c...

1. DERIVED GEOMETRY WITH L∞ ALGEBRAS We are interested in studying formal derived moduli problems, as an orienting remark recall that particularly nice simplicial sets are those that are Kan complexes and that the nerve of a category C is Kan complex if and only if C is a groupoid. Consider the following progression. • Schemes: Functors from commutative algebras to sets; • Stacks: Functors from...

This paper describes some basic relationships between mathematical structures that are relevant in quantum logic and probability, namely convex sets, effect algebras, and a new class of functors that we call ‘convex functors’; they include what are usually called probability distribution functors. These relationships take the form of three adjunctions. Two of these three are ‘dual’ adjunctions ...

For a “genuine” equivariant commutative ring spectrum R, π0(R) admits a rich algebraic structure known as a Tambara functor. This algebraic structure mirrors the structure on R arising from the existence of multiplicative norm maps. Motivated by the surprising fact that Bousfield localization can destroy some of the norm maps, in previous work we studied equivariant commutative ring structures ...

The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a Morita context comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Mor...

Applicative functors define an interface to computation that is more general, and correspondingly weaker, than that of monads. First used in parser libraries, they are now seeing a wide range of applications. This paper sets out to explore the space of non-monadic applicative functors useful in programming. We work with a generalization, lax monoidal functors, and consider several methods of co...

We construct a family of functors assigning an R-module to a flag of R-modules, where R is a commutative ring. As particular instances, we get flagged Schur functors and Schubert functors, the latter family being indexed by permutations. We identify Schubert functors for vexillary permutations with some flagged Schur functors, thus establishing a functorial analogue of a theorem from [6] and [1...