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Lecture

Construction of Free Action Functor

Related concepts (26)

Étale morphism

In algebraic geometry, an étale morphism (etal) is a morphism of schemes that is formally étale and locally of finite presentation. This is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem, but because open sets in the Zariski topology are so large, they are not necessarily local isomorphisms. Despite this, étale maps retain many of the properties of local analytic isomorphisms, and are useful in defining the algebraic fundamental group and the étale topology.

Mathematical diagram

Mathematical diagrams, such as charts and graphs, are mainly designed to convey mathematical relationships—for example, comparisons over time. A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram The complex plane is sometimes called the Argand plane because it is used in Argand diagrams. These are named after Jean-Robert Argand (1768–1822), although they were first described by Norwegian-Danish land surveyor and mathematician Caspar Wessel (1745–1818).

Diagram

A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word graph is sometimes used as a synonym for diagram.

Morphism of algebraic varieties

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called a regular map. A morphism from an algebraic variety to the affine line is also called a regular function. A regular map whose inverse is also regular is called biregular, and the biregular maps are the isomorphisms of algebraic varieties.

Free will

Free will is the notional capacity or ability to choose between different possible courses of action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgements which apply only to actions that are freely chosen. It is also connected with the concepts of advice, persuasion, deliberation, and prohibition. Traditionally, only actions that are freely willed are seen as deserving credit or blame.

Free will in theology

Free will in theology is an important part of the debate on free will in general. Religions vary greatly in their response to the standard argument against free will and thus might appeal to any number of responses to the paradox of free will, the claim that omniscience and free will are incompatible. Argument from free will The theological doctrine of divine foreknowledge is often alleged to be in conflict with free will, particularly in Calvinistic circles: if God knows exactly what will happen (right down to every choice a person makes), it would seem that the "freedom" of these choices is called into question.