Related papers: A Generalised Exactness Structure for Sets

We present a detailed synthetic overview of the utilisation of categorical techniques in the study of order structures together with their applications in operational quantum theory. First, after reviewing the notion of residuation and its…

We define the notion of exact completion with respect to an existential elementary doctrine. We observe that the forgetful functor from the 2-category exact categories to existential elementary doctrines has a left biadjoint that can be…

This paper describes several cases of adjunction in the homomorphism preorder of relational structures. We say that two functors $\Lambda$ and $\Gamma$ between thin categories of relational structures are adjoint if for all structures…

We construct a functor from the category of graphs to the category of groups which is faithful and "almost" full, in the sense that it induces bijections of the Hom sets up to trivial homomorphisms and conjugation in the category of groups.…

Everyone knows that if you have a bivariant homology theory satisfying a base change formula, you get an representation of a category of correspondences. For theories in which the covariant and contravariant transfer maps are in mutual…

We define a Galois structure on the category of pairs of equivalence relations in an exact Mal'tsev category, and characterize central and double central extensions in terms of higher commutator conditions. These results generalize both the…

We generalize the classical notion of adjoint of a linear operator and the Aron-Schottenloher notion of adjoint of a homogeneous polynomial. The general notion is shown to enjoy several properties enjoyed by the classical ones, nevertheless…

We show that contrary to appearances, Multimodal Type Theory (MTT) over a 2-category M can be interpreted in any M-shaped diagram of categories having, and functors preserving, M-sized limits, without the need for extra left adjoints. This…

Given an adjoint pair of functors $F,G$, the composite $GF$ naturally gets the structure of a monad. The same monad may arise from many such adjoint pairs of functors, however. Can one describe all of the adjunctions giving rise to a given…

Voevodsky's derived category of motives is the main arena today for the study of algebraic cycles and motivic cohomology. In this paper we study whether the inclusions of three important subcategories of motives have a left or right…

Let $G$ be a group. Two elements $x,y \in G$ are said to be in the same $z$-class if their centralizers in $G$ are conjugate within $G$. Consider $\mathbb F$ a perfect field of characteristic $\neq 2$, which has a non-trivial Galois…

We investigate Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads to a…

For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…

To a function with values in the power set of a pre--ordered, separated locally convex space a family of scalarizations is given which completely characterizes the original function. A concept of a Legendre--Fenchel conjugate for set-valued…

We exhibit an adjunction between a category of abstract algebras of partial functions and a category of set quotients. The algebras are those atomic algebras representable as a collection of partial functions closed under relative…

We give a construction of triangulated categories as quotients of exact categories where the subclass of objects sent to zero is defined by a triple of functors. This includes the cases of homotopy and stable module categories. These…

Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…

There are many contexts in algebraic geometry, algebraic topology, and homological algebra where one encounters a functor that has both a left and right adjoint, with the right adjoint being isomorphic to a shift of the left adjoint…

The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…

Two distinct projections of finite rank $m$ are adjacent if their difference is an operator of rank two or, equivalently, the intersection of their images is $(m-1)$-dimensional. We extend this adjacency relation on other conjugacy classes…