6 papers
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…
An embedding theorem for regular Mal'tsev categories
Pierre-Alain Jacqmin
In this paper, we obtain a non-abelian analogue of Lubkin's embedding theorem for abelian categories. Our theorem faithfully embeds any small regular Mal'tsev category …
Bipullbacks of fractions and the snail lemma
P. -A. Jacqmin, S. Mantovani, G. Metere +1
We establish conditions giving the existence of bipullbacks in bicategories of fractions. We apply our results to construct a - exact sequence associated with a fractor b…
On fibrations between internal groupoids
P. -A. Jacqmin, S. Mantovani, G. Metere +1
In order to deduce the internal version of the Brown exact sequence from the internal version of the Gabriel-Zisman exact sequence, we characterize fibrations and -fibrations…