A notion of a coring extension is defined and it is shown to be equivalent to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable functors is illustrated by functors between categories of descent data. A category in which objects are corings and morphisms are coring extensions...

A common theme in algebraic topology is to study functors from the homotopy category of topological spaces to various categories of algebraic objects, such as the classical homology functor, the cohomology functor and the homopoty functor. In this talk, I will introduce some functors from topological spaces to Lie algebras and algebraic varieties, and explore their properties. We can use these ...

In the following note we characterize the category of Mackey-functors from a category ~, satisfying a few assumptions, to a category ~ as the category of functors from Sp(~), the category of "spans" in ~, to ~ which preserve finite products. This caracterization permits to apply all results on categories of functors preserving a given class of limits to the case of Mackey-functors. We recall (c...

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 ...