Zobrazeno 1 - 10
of 105
pro vyhledávání: '"MONTOLI, ANDREA"'
We compare the concepts of protomodular and weakly protomodular objects within the context of unital categories. Our analysis demonstrates that these two notions are generally distinct. To establish this, we introduce left pseudocancellative unital m
Externí odkaz:
http://arxiv.org/abs/2409.19076
We study the categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, and studying some exactness properties. We show that, from an algebraic point of view, the category of right-preor
Externí odkaz:
http://arxiv.org/abs/2406.10071
Autor:
Cappelletti, Andrea, Montoli, Andrea
We show that non-pointed versions of the classical homological lemmas hold in regular protomodular categories equipped with a suitable posetal monocoreflective subcategory. Examples of such categories are all protomodular varieties of universal algeb
Externí odkaz:
http://arxiv.org/abs/2405.11038
Our main focus concerns a possible lax version of the algebraic property of protomodularity for Ord-enriched categories. Our motivating example is the category OrdAb of preordered abelian groups; indeed, while abelian groups form a protomodular categ
Externí odkaz:
http://arxiv.org/abs/2210.14332
Publikováno v:
Theory Appl. Categ. 36 (2021), no. 18, 514--555
Motivated by the categorical-algebraic analysis of split epimorphisms of monoids, we study the concept of a special object induced by the intrinsic Schreier split epimorphisms in the context of a regular unital category with binary coproducts, comona
Externí odkaz:
http://arxiv.org/abs/2102.05877
We consider compatible group structures on a $V$-category, where $V$ is a quantale, and we study the topological and algebraic properties of such groups. Examples of such structures are preordered groups, metric and ultrametric groups, probabilistic
Externí odkaz:
http://arxiv.org/abs/2005.07738
Publikováno v:
Appl. Categ. Structures 28 (2020), 517--538
In the context of regular unital categories we introduce an intrinsic version of the notion of a Schreier split epimorphism, originally considered for monoids. We show that such split epimorphisms satisfy the same homological properties as Schreier s
Externí odkaz:
http://arxiv.org/abs/1911.08770
Autor:
Bourn, Dominique, Montoli, Andrea
We investigate what is remaining of the 3x3 lemma and of the denormalized 3x3 lemma, respectively valid in a pointed protomodular and in a Maltsev category, in the context of partial pointed protomodular and partial Maltsev categories, relatively to
Externí odkaz:
http://arxiv.org/abs/1801.09104
Publikováno v:
Logical Methods in Computer Science, Volume 13, Issue 3 (September 1, 2017) lmcs:2552
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion of S-proto
Externí odkaz:
http://arxiv.org/abs/1611.09148
Publikováno v:
J. Pure Appl. Algebra 222 (2018), No. 4, 747-777
The aim of this paper is to solve a problem proposed by Dominique Bourn: to provide a categorical-algebraic characterisation of groups amongst monoids and of rings amongst semirings. In the case of monoids, our solution is given by the following equi
Externí odkaz:
http://arxiv.org/abs/1606.08649