fields, chris glazebrook, james f.

Descriptions of measurement typically neglect the observations required to identify the apparatus employed to either prepare or register the final state of the &ldquo / system of interest.&rdquo / Here, we employ category-theoretic methods, particularly the theory of classifiers, to characterize the full interaction between observer and world in te...

Wehrung, Friedrich

We construct a completely normal bounded distributive lattice D in which for every pair (a, b) of elements, the set {x ∈ D | a ≤ b ∨ x} has a countable coinitial subset, such that D does not carry any binary operation - satisfying the identities x ≤ y ∨(x-y),(x-y)∧(y-x) = 0, and x-z ≤ (x-y)∨(y-z). In particular, D is not a homomorphic image of the ...

Wehrung, Friedrich

Anti-elementarity is a strong way of ensuring that a class of structures , in a given first-order language, is not closed under elementary equivalence with respect to any infinitary language of the form L ∞λ. We prove that many naturally defined classes are anti-elementary, including the following: • the class of all lattices of finitely generated ...

Gillibert, Pierre Wehrung, Friedrich

Healy, Michael John Caudell, Thomas Preston
Published in
Axiomathes

We propose category theory, the mathematical theory of structure, as a vehicle for defining ontologies in an unambiguous language with analytical and constructive features. Specifically, we apply categorical logic and model theory, based upon viewing an ontology as a sub-category of a category of theories expressed in a formal logic. In addition to...

Wehrung, Friedrich
Published in
algebra universalis

We prove a general categorical theorem that enables us to state that under certain conditions, the range of a functor is large. As an application, we prove various results of which the following is a prototype: If every diagram, indexed by a lattice, of finiteBoolean 〈∨ ,0 〉-semilattices with 〈∨ ,0 〉-embeddings, can be lifted, with respect to the C...

Wehrung, Friedrich

A (v,0)-semilattice is ultraboolean, if it is a directed union of finite Boolean (v,0)-semilattices. We prove that every distributive (v,0)-semilattice is a retract of some ultraboolean (v,0)-semilattices. This is established by proving that every finite distributive (v,0)-semilattice is a retract of some finite Boolean (v,0)-semilattice, and this ...

Ehresmann, Andrée C.
Published in
Applied Categorical Structures

The notion of the root of the category, which is a minimal (in a precise sense) weakly coreflective subcategory, is introduced in view of defining ‘local’ solutions of universal problems: If U is a functor from C′ to C and c an object of C, the root of the comma-category c|U is called a U-universal root generated by c; when it exists, it is unique ...

Oriat, Catherine

La composition de spécifications modulaires peut être modélisée, dans le formalisme des catégories, par des colimites de diagrammes. La somme amalgamée permet en particulier d'assembler deux spécifications en précisant les parties communes. Notre travail poursuit cette idée classique selon trois axes. D'un point de vue syntaxique, nous définissons ...

Bashir, Robert El Kepka, Tomáš Němec, Petr
Published in
Czechoslovak Mathematical Journal

For every module M we have a natural monomorphism \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\Psi :\coprod\limits_{i \in I} {{\text{Hom}}_R \left( {M,A_i } \right...