Search results
Results from the WOW.Com Content Network
A topological space is sometimes said to exhibit a property locally, if the property is exhibited "near" each point in one of the following ways: Each point has a neighborhood exhibiting the property; Each point has a neighborhood base of sets exhibiting the property.
If q is the cardinality of the residue field, the absolute value on F induced by its structure as a local field is given by: [6] | a | = q − v ( a ) . {\displaystyle |a|=q^{-v(a)}.} An equivalent and very important definition of a non-Archimedean local field is that it is a field that is complete with respect to a discrete valuation and whose ...
An algebraic group is a group object in the category of algebraic varieties. In modern algebraic geometry, one considers the more general group schemes, group objects in the category of schemes. A localic group is a group object in the category of locales. The group objects in the category of groups (or monoids) are the abelian groups.
Given a groupoid object (R, U), the equalizer of , if any, is a group object called the inertia group of the groupoid. The coequalizer of the same diagram, if any, is the quotient of the groupoid. Each groupoid object in a category C (if any) may be thought of as a contravariant functor from C to the category of groupoids.
Instead of two objects, we can start with an arbitrary family of objects indexed by a set .. Given a family () of objects, a product of the family is an object equipped with morphisms :, satisfying the following universal property:
Bell established a criterion to distinguish between local hidden-variables theory and quantum theory by measuring specific values of correlations between entangled particles. Subsequent experimental tests have shown that some quantum effects do violate Bell's inequalities and cannot be reproduced by a local hidden-variables theory. [5]
In mathematics, the idea of a free object is one of the basic concepts of abstract algebra.Informally, a free object over a set A can be thought of as being a "generic" algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.
with the following property: For each monomorphism j: U → X there is a unique morphism χ j: X → Ω such that the following commutative diagram is a pullback diagram—that is, U is the limit of the diagram: The morphism χ j is then called the classifying morphism for the subobject represented by j.