44 citations · 82 across the 30 of their papers we have counts for
23 papers · 1 filter
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; (…
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…
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…
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…
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…
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…
Further remarks on the "Smith is Huq" condition
Nelson Martins-Ferreira, Tim Van der Linden
We compare the 'Smith is Huq' condition (SH) with three commutator conditions in semi-abelian categories: first an apparently weaker condition which arose in joint work with Bourn…
An observation on n-permutability
Nelson Martins-Ferreira, Diana Rodelo, Tim Van der Linden
We prove that in a regular category all reflexive and transitive relations are symmetric if and only if every internal category is an internal groupoid. In particular, these condit…
A decomposition formula for the weighted commutator
Nelson Martins-Ferreira, Tim Van der Linden
We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.
On algebraic and more general categories whose split epimorphisms have underlying product projections
James R. A. Gray, Nelson Martins-Ferreira
We characterize those varieties of universal algebras where every split epimorphism considered as a map of sets is a product projection. In addition we obtain new characterizations…
Categories vs. groupoids via generalised Mal'tsev properties
Nelson Martins-Ferreira, Tim Van der Linden
We study the difference between internal categories and internal groupoids in terms of generalised Mal'tsev properties---the weak Mal'tsev property on the one hand, and -permuta…
A note on the "Smith is Huq" condition
Nelson Martins-Ferreira, Tim Van der Linden
We show that two known conditions which arose naturally in commutator theory and in the theory of internal crossed modules coincide: every star-multiplicative graph is multiplicati…
Internal precategories relative to split epimorphisms
N. Martins-Ferreira
For a given category B we are interested in studying internal categorical structures in B. This work is the starting point, where we consider reflexive graphs and precategories (i.…
On the notion of pseudocategory internal to a category with a 2-cell structure
N. Martins-Ferreira
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equ…