Galois connections as left adjoint maps
Galois lattice as a framework to specify building class hierarchies algorithms
Galois Lattice as a Framework to Specify Building Class Hierarchies Algorithms
In the context of object-oriented systems, algorithms for building class hierarchies are currently receiving much attention. We present here a characterization of several global algorithms. A global algorithm is one which starts with only the set of classes (provided with all their properties) and directly builds the hierarchy. The algorithms scrutinized were developped each in a different framework. In this survey, they are explained in a single framework, which takes advantage of a substructure...
Galois theory for groups
Galois triangle theory for direct summands of modules
Galois-type connections and closure operations on preordered sets.
General algebraic geometry and formal concept analysis.
Going down in (semi)lattices of finite Moore families and convex geometries
In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have the same poset of join-irreducible elements. We show that this set—ordered by set inclusion—is a ranked join-semilattice and we...
Gram-Schmidt's orthogonalization based on the concept of generalized orthogonality
Group actions on Cartesian powers with applications to represenation theory.