44 citations · 82 across the 30 of their papers we have counts for
32 papers
Internal groupoids as involutive-2-links
Nelson Martins-Ferreira
Regardless of its environment, the category of internal groupoids is shown to be equivalent to the full subcategory of involutive-2-links that are unital and associative. The new n…
What is an internal groupoid?
Nelson Martins-Ferreira
An answer to the question investigated in this paper brings a new characterization of internal groupoids such that: (a) it holds even when finite limits are not assumed to exist; (…
Weakly Schreier extensions for general algebras
Graham Manuell, Nelson Martins-Ferreira
Weakly Schreier split extensions are a reasonably large, yet well-understood class of monoid extensions, which generalise some aspects of split extensions of groups. This short not…
On the normality of monoid monomorphisms
Nelson Martins-Ferreira, Manuela Sobral
In the category of monoids we characterize monomorphisms that are normal, in an appropriate sense, to internal reflexive relations, preorders or equivalence relations. The zero-cla…
On semibiproducts of magmas and semigroups
Nelson Martins-Ferreira
A generalization to the categorical notion of biproduct, called semibiproduct, which in the case of groups covers classical semidirect products, has recently been analysed in the c…
Pointed semibiproducts of monoids
Nelson Martins-Ferreira
Semibiproducts of monoids are introduced here as a common generalization to biproducts (of abelian groups) and to semidirect products (of groups) for exploring a wide class of mono…
A refinement of ternary Boolean algebras
J. P. Fatelo, N. Martins-Ferreira
An algebraic structure with two constants and one ternary operation, which is not completely commutative, is put forward to accommodate ternary Boolean algebras. When the ternary o…
Semi-biproducts of monoids
Nelson Martins-Ferreira
It is shown that the category of \emph{semi-biproducts} of monoids is equivalent to the category of \emph{pseudo-actions}. A semi-biproduct of monoids is a new notion, obtained thr…
Affine mobi spaces
J. P. Fatelo, N. Martins-Ferreira
The category of mobi algebras has been introduced as a model to the unit interval of real numbers. The notion of mobi space over a mobi algebra has been proposed as a model for spa…
A new look at Ternary Boolean Algebras
J. P. Fatelo, N. Martins-Ferreira
We present a new approach to ternary Boolean algebras in which negation is derived from the ternary operation. The key aspect is the replacement of complete commutativity by other…
On the structure of topological spaces
Nelson Martins-Ferreira
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders…
Mobility spaces and geodesics for the n-sphere
J. P. Fatelo, N. Martins-Ferreira
We introduce an algebraic system which can be used as a model for spaces with geodesic paths between any two of their points. This new algebraic structure is based on the notion of…
Schreier split extensions of preordered monoids
Nelson Martins-Ferreira, Manuela Sobral
Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories of the category of preordered monoid…
Semi-biproducts in monoids
Nelson Martins-Ferreira
It is shown that the category of semi-biproducts in monoids is equivalent to a category of pseudo-actions. A semi-biproduct in monoids is at the same time a generalization of a sem…
Mobility spaces and their geodesic paths
J. P. Fatelo, N. Martins-Ferreira
We introduce an algebraic system which can be used as a model for spaces with geodesic paths between any two of their points. This new algebraic structure is based on the notion of…
The Lawvere condition and a classification theorem for Mal'tsev categories
Nelson Martins-Ferreira
A classification theorem for three different sorts of Mal'tsev categories is proven. The theorem provides a classification for Mal'tsev category, naturally Malt'sev category, and w…
Cancellative conjugation semigroups and monoids
A. P. Garrão, N. Martins-Ferreira, M. Raposo +1
We show that the category of cancellative conjugation semigroups is weakly Mal'tsev and give a characterization of all admissible diagrams there. In the category of cancellative co…
The Category of Crossed Modules of Crossed Modules and Its Associated Double Groupoids
Nelson Martins-Ferreira, Ahmet Emin Tatar
In this work we study the notion of Whitehead sequence in the category of crossed modules and actions of crossed modules. As expected, Whitehead sequences in that context are the s…
Mobi algebra as an abstraction to the unit interval and its comparison to rings
J. P. Fatelo, N. Martins-Ferreira
We begin by introducing an algebraic structure with three constants and one ternary operation to which we call mobi algebra. This structure has been designed to capture the most re…
On some categorical-algebraic conditions in S-protomodular categories
Nelson Martins-Ferreira, Andrea Montoli, Manuela Sobral
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 cart…
What is an ideal a zero-class of?
N. Martins-Ferreira, A. Montoli, A. Ursini +1
We characterise, in pointed regular categories, the ideals as the zero-classes of surjective relations. Moreover, we study a variation of the "Smith is Huq" condition: two surjecti…
Internal bicategories in groups
Nelson Martins-Ferreira
A detailed description of internal bicategory in the category of groups is derived from the general description of internal bicategories in weakly Mal'tsev sesquicategories. The ex…
Crossed-modules and Whitehead sequences
Nelson Martins-Ferreira
We introduce the notion of Whitehead sequence which is defined for a base category together with a system of abstract actions over it. In the classical case of groups and group act…
Internal monoids and groups in the category of commutative cancellative medial magmas
Jorge P. Fatelo, Nelson Martins-Ferreira
This article considers the category of commutative medial magmas with cancellation, a structure that generalizes midpoint algebras and commutative semigroups with cancellation. In…