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Qu'est-ce (qui) est functorial subgroup - définition

CONCEPT IN CATEGORY THEORY

Functorial point

Normal subgroup

SUBGROUP INVARIANT UNDER CONJUGATION

Normal subgroups; Invariant subgroup; ◅; Normal group; ⊲; ⊳; ⊴; ⊵; ⋪; ⋫; ⋬; ⋭; Normal Subgroup; Self-conjugate subgroup

In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation by members of the group of which it is a part. In other words, a subgroup N of the group G is normal in G if and only if gng^{-1} \in N for all g \in G and n \in N.

https://en.wikipedia.org/wiki/Normal_subgroup

Commutator subgroup

SMALLEST NORMAL SUBGROUP BY WHICH THE QUOTIENT IS COMMUTATIVE

Derived subgroup; Abelianisation; Abelianization; Derived group; Derived series; Transfinite derived series; The Commutator Subgroup Of G; The Derived Group Of G; Commutator group

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

https://en.wikipedia.org/wiki/Commutator_subgroup

Subgroup

SUBSET OF A MATHEMATICAL GROUP THAT FORMS A GROUP ITSELF

SubGroup; Subgroups; Proper subgroup; Overgroup; Subgroup test; Subgroup Test; Sub-group; Subgroup (mathematics); Subgroups of S4

·noun A subdivision of a group, as of animals.

Wikipédia

Element (category theory)

In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category. This idea often allows restating of definitions or properties of morphisms (such as monomorphism or product) given by a universal property in more familiar terms, by stating their relation to elements. Some very general theorems, such as Yoneda's lemma and the Mitchell embedding theorem, are of great utility for this, by allowing one to work in a context where these translations are valid. This approach to category theory – in particular the use of the Yoneda lemma in this way – is due to Grothendieck, and is often called the method of the functor of points.

https://en.wikipedia.org/wiki/Element (category theory)