5 citations · 6 across the 13 of their papers we have counts for
15 papers
A note on coextensivity of bounded hoops
Michael Hoefnagel, Giuseppe Metere, Danielle Kleyn
The main aim of this note is to provide a characterisation of coextensive morphisms in the category of bounded hoops. This characterisation is then used to show that several catego…
Abelian objects in categories with normal projections
Michael Hoefnagel, Zurab Janelidze
It is known that in (regular) unital and in subtractive categories, internal abelian groups are simply behaved; e.g., they are the same as internal algebras satisfying $s(x…
On extensivity of morphisms
Michael Hoefnagel, Emma Theart
Extensivity of a category may be described as a property of coproducts in the category, namely, that they are disjoint and universal. An alternative viewpoint is that it is a prope…
Partial algebras and implications of (weak) matrix properties
Michael Hoefnagel, Pierre-Alain Jacqmin
Matrix properties are a type of property of categories which includes the ones of being Mal'tsev, arithmetical, majority, unital, strongly unital and subtractive. Recently, an algo…
A note on the atomicity of arithmeticity
Michael Hoefnagel, Pierre-Alain Jacqmin
The main aim of this note is to show that, in the regular context, every matrix property in the sense of Z. Janelidze either implies the Mal'tsev property, or is implied by the maj…
Categorical aspects of congruence distributivity
Michael Hoefnagel, Diana Rodelo
We study a categorical condition on relations, which is a categorical formulation of Jónsson's characterisation of congruence distributive varieties. Categories satisfying these co…
Centrality and the commutativity of finite products with coequalisers
Michael Hoefnagel
We study centrality of morphisms in a setting derived from that of a pointed category in which binary products commute with coequalisers. The main results of this paper show that m…
When a matrix condition implies the Mal'tsev property
Michael Hoefnagel, Pierre-Alain Jacqmin
Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in…
Matrix taxonomy and Bourn localization
Michael Hoefnagel, Pierre-Alain Jacqmin
In a recent paper, an algorithm has been presented for determining implications between a particular kind of category theoretic property represented by matrices -- the so called `m…
The matrix taxonomy of finitely complete categories
Michael Hoefnagel, Pierre-Alain Jacqmin, Zurab Janelidze
This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represente…
Anticommutativity and the triangular lemma
Michael Hoefnagel
For a variety , it has been recently shown that binary products commute with arbitrary coequalizers locally, i.e., in every fibre of the fibration of points $π: \mathr…
Products and coequalizers in pointed categories
Michael Hoefnagel
In this paper, we investigate the property (P) that finite products commute with arbitrary coequalizers in pointed categories. Examples of such categories include any regular unita…
-coextensivity and the strict refinement property
Michael Hoefnagel
The notion of an -coextensive object is introduced in an arbitrary category , where is a distinguished class of morphisms from .…
Characterizations of majority categories
Michael Hoefnagel
In universal algebra, it is well known that varieties admitting a majority term admit several Mal'tsev-type characterizations. The main aim of this paper is to establish categorica…
Majority categories
Michael Anton Hoefnagel
We introduce the notion of a majority category --- the categorical counterpart of varieties of universal algebras admitting a majority term. This notion can be thought to capture p…