Loading...
41 results
Search Results
Now showing 1 - 10 of 41
- Curvas geodésicas : um exemplo com resolução analíticaPublication . Fatelo, J. P.; Martins-Ferreira, N.Apresentamos um exemplo de uma superfície não trivial em R3 na qual as curvas geodésicas são encontradas analiticamente.
- On the categorical behaviour of preordered groupsPublication . Clementino, Maria Manuel; Martins-Ferreira, Nelson; Montoli, AndreaWe study the categorical properties of preordered groups. We first give a description of limits and colimits in this category, and study some classical exactness properties. Then we point out a strong analogy between the algebraic behaviour of preordered groups and monoids, and we apply two different recent approaches to relative categorical algebra to obtain some homological properties of preordered groups.
- Optimization of toolpath trajectories on arbitrary surfacesPublication . Gaspar, Miguel; Martins-Ferreira, N.Given an arbitrary region on the plane, modelled as a graph with a symmetry, we describe a procedure to find the best orientation for slicing, via a zigzag tool-path trajectory based curve, in order to minimize its discontinuities. We also develop some directions on how to generalize the procedure up to the level of optimizing tool-path trajectories on arbitrary surfaces rather than planar regions only.
- Mobi algebra as an abstraction to the unit interval and its comparison to ringsPublication . Fatelo, J. P.; Martins-Ferreira, NelsonWe introduce a new algebraic structure, called mobi algebra, consisting of three constants and one ternary operation. The canonical example of a mobi algebra is the unit interval with the three constants 0, 1, and 1/2 and the ternary operation given by the formula x−yx+yz. We study some of its properties and prove that every unitary ring with one half uniquely determines and is uniquely determined by a mobi algebra with one double. Another algebraic structure, called involutive medial monoid (IMM), is considered to establish the passage between rings and mobi algebras.
- On the classification of Schreier extensions of monoids with non-abelian kernelPublication . Martins-Ferreira, Nelson; Montoli, Andrea; Patchkoria, Alex; Sobral, ManuelaWe show that any regular (right) Schreier extension of a monoid M by a monoid A induces an abstract kernel Φ: M → End(A)/Inn(A) . If an abstract kernel factors through SEnd(A)/Inn(A) , where SEnd(A) is the monoid of surjective endomorphisms of A, then we associate to it an obstruction, which is an element of the third cohomology group of M with coefficients in the abelian group U(Z(A)) of invertible elements of the center Z(A) of A, on which M acts via Φ. An abstract kernel Φ: M → SEnd(A)/Inn(A) (resp. Φ: M → Aut(A)/Inn(A) ) is induced by a regular weakly homogeneous (resp. homogeneous) Schreier extension of M by A if and only if its obstruction is zero.We also show that the set of isomorphism classes of regular weakly homogeneous (resp. homogeneous) Schreier extensions inducing a given abstract kernel Φ: M → SEnd(A)/Inn(A) (resp. Φ: M → Aut(A)/Inn(A) ), when it is not empty, is in bijection with the second cohomology group of M with coefficients in U(Z(A)).
- A unified classification theorem for Mal’tsev-like categoriesPublication . Martins-Ferreira, NelsonIn this paper we give unified characterizations of categories defined by variations of theMal’tsev property.
- Crossed modules and Whitehead sequencesPublication . Martins-Ferreira, NelsonWe introduce the notion ofWhitehead 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 actions theWhitehead sequences are precisely the crossed modules of groups. For a general setting we give sufficient conditions for the existence of a categorical equivalence between internal groupoids and Whitehead sequences.
- On some categorical-algebraic conditions in S-protomodular categoriesPublication . Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, ManuelaIn 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-protomodular category, whose main examples are the category of monoids and, more generally, categories of monoids with operations and Jo\'{o}nsson-Tarski varieties, raises a similar question: how to get a description of S-protomodular categories with a strong monoid-like behavior. In this paper we consider relative versions of the conditions mentioned above, in order to exhibit the parallelism with the "absolute" protomodular context and to obtain a hierarchy among S-protomodular categories.
- Baer sums of special Schreier extensions of monoidsPublication . Martins-Ferreira, Nelson; Montoli, Andrea; Sobral, ManuelaWe show that the special Schreier extensions of monoids, with abelian kernel, admit a Baer sum construction, which generalizes the classical one for group extensions with abelian kernel. In order to do that, we characterize the special Schreier extensions by means of factor sets.
- Schreier split extensions of preordered monoidsPublication . Martins-Ferreira, N.; Sobral, M.Properties of preordered monoids are investigated and important subclasses of such structures are studied. The corresponding full subcategories are related between them by appropriate functors as well as with the categories of preordered sets and of monoids. Schreier split extensions are described in the full subcategory of preordered monoids whose preorder is determined by the corresponding positive cone.