Related papers: The core of adjoint functors

We introduce a new logic that combines Adjoint Logic with Graded Necessity Modalities. This results in a very expressive system capable of controlling when and how structural rules are used. We give a sequent calculus, natural deduction,…

Let $(\mathcal{A},\mathcal{E})$ be an exact category. We establish basic results that allow one to identify sub(bi)functors of $\operatorname{Ext}_{\mathcal{E}}(-,-)$ using additivity of numerical functions and restriction to subcategories.…

For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.

This article defines a complement of a function and conditions for existence of such a complement function and presents few algorithms to construct a complement.

We build an explicit link between coherent functors in the sense of Auslander and strict polynomial functors in the sense of Friedlander and Suslin. Applications to functor cohomology are discussed.

We present a logical and algebraic description of right adjoint functors between generalized quasi-varieties, inspired by the work of McKenzie on category equivalence. This result is achieved by developing a correspondence between the…

The basic notions of category theory, such as limit, adjunction, and orthogonality, all involve assertions of the existence and uniqueness of certain arrows. Weak notions arise when one drops the uniqueness requirement and asks only for…

It is characterized when coarsening functors between categories of graded modules preserve injectivity of objects, and when they commute with graded covariant Hom functors.

Diers developed a general theory of right multi-adjoint functors leading to a purely categorical, point-set construction of spectra. Situations of multiversal properties return sets of canonical solutions rather than a unique one. In the…

This paper synergizes the roles of adjoint in various disciplines of mathematics, sciences, and engineering. Though the materials developed and presented are not new -- as each or some could be found in (or inferred from) publications in…

We describe a procedure for constructing morphisms in additive categories, combining Auslander's concept of a morphism determined by an object with the existence of flat covers. Also, we show how flat covers are turned into projective…

An adjoint pair of contravariant functors between abelian categories can be extended to the adjoint pair of their derived functors in the associated derived categories. We describe the reflexive complexes and interpret the achieved results…

We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…

Building on techniques used in the case of the disc, we use a variety of methods to develop formulae for the adjoints of composition operators on Hardy spaces of the upper half-plane. In doing so, we prove a slight extension of a known…

We study the bicategory of Landau-Ginzburg models, which has potentials as objects and matrix factorisations as 1-morphisms. Our main result is the existence of adjoints in this bicategory and a description of evaluation and coevaluation…

In this paper we investigate the categories of braided objects, algebras and bialgebras in a given monoidal category, some pairs of adjoint functors between them and their relations. In particular we construct a braided primitive functor…

All components of complements of discriminant varieties of simple real function singularities are explicitly listed. New invariants of such components (for not necessarily simple singularities) are introduced. A combinatorial algorithm…

For each pair of lax-idempotent pseudomonads $R$ and $I$, for which $I$ is locally fully faithful and $R$ distributes over $I$, we establish an adjoint functor theorem, relating $R$-cocontinuity to adjointness relative to $I$. This provides…

We prove a classification of additive polynomial superfunctors, which allows us to compute some extensions of a superfunctor of the form $F \circ A$ where $F$ is a classical polynomial functor and $A$ is additive. We get a formula which…

We show that differential calculus (in its usual form, or in the general form of topological differential calculus) can be fully imdedded into a functor category (functors from a small category of anchord tangent algebras to anchored sets).…