Bifunctors and adjoint pairs

Discretization by adjoint pairs: Lukasiewicz and Q-module transforms

We define the Lukasiewicz Transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing. We also propose a strong extension of such concepts and results in the framework of quantales and quantale modules. 1 The Lukasiewicz transform and its applications Th...

Bousfield Localisations along Quillen Bifunctors

Adjoint Pairs for Quasi-coherent Sheaves on Stacks

In this paper we construct a pushforward-pullback adjoint pair for categories of quasi-coherent sheaves, along a morphism of algebraic stacks, which is represented in algebraic stacks over the site C = Affflat. The construction uses the characterization of algebraic stacks of [H3] and is based on the descent description of the category of quasi-coherent sheaves given in [H2]. We show that an es...

Comparison of spectral sequences involving bifunctors

Suppose given functors A × A F B G C between abelian categories, an object X in A and an object X ′ in A such that F (X,−), F (−,X ) and G are left exact, and such that further conditions hold. We show that, E1-terms exempt, the Grothendieck spectral sequence of the composition of F (X,−) and G evaluated at X ′ is isomorphic to the Grothendieck spectral sequence of the composition of F (−,X ) a...

The Abstract Titchmarsh-weyl M-function for Adjoint Operator Pairs and Its Relation to the Spectrum

In the setting of adjoint pairs of operators we consider the question: to what extent does the Weyl M -function see the same singularities as the resolvent of a certain restriction AB of the maximal operator? We obtain results showing that it is possible to describe explicitly certain spaces S and S̃ such that the resolvent bordered by projections onto these subspaces is analytic everywhere that...