9 papers · 1 filter
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 syntactic characterization of weakly Mal'tsev varieties
Nadja Egner, Pierre-Alain Jacqmin, Nelson Martins-Ferreira
The notion of a weakly Mal'tsev category, as it was introduced in 2008 by the third author, is a generalization of the classical notion of a Mal'tsev category. It is well-known tha…
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…
On stability of exactness properties under the pro-completion
Pierre-Alain Jacqmin, Zurab Janelidze
In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and give…
On the naturalness of Mal'tsev categories
Dominique Bourn, Marino Gran, Pierre-Alain Jacqmin
Mal'tsev categories turned out to be a central concept in categorical algebra. On one hand, the simplicity and the beauty of the notion is revealed through a lot of characterizatio…
Finiteness spaces and generalized power series
Richard Blute, Robin Cockett, Pierre-Alain Jacqmin +1
We consider Ribenboim's construction of rings of generalized power series. Ribenboim's construction makes use of a special class of partially ordered monoids and a special class of…