group in nLab
1. Definition. A group is an algebraic structure consisting of a set G G and a binary operation ⋆ \star that satisfies the group axioms, being:.
A group object or internal group internal to a category C \mathcal{C} with finite products (binary Cartesian products and a terminal object * \ast )
Eugene P. Wigner: Group theory: And its application to the quantum mechanics of atomic spectra, 5, Academic Press (1959)
Grp Grp is the category with groups as objects and group homomorphisms as morphisms. Similarly there there is the full subcategory FinGrp ...
The theory of group presentations generalises to that of presentations of monoids and then to general rewriting systems.
1. Definition. Definition 1.1. For R R a ring, its group of units, denoted R × R^\times or GL 1 ( R ) GL_1(R) , is the group whose elements are ...
Motivation for the nLab's definition of cohomology?
How exactly does Verdier's hypercovering result make sheaf cohomology satisfy nLab's definition? For group cohomology, the nLab says: For ...
The group algebra of a group G G over a ring R R is the associative algebra whose elements are formal linear combinations over R R of the ...
The nLab is a wiki for research-level notes, expositions and collaborative work, including original research, in mathematics, physics, and philosophy, ...
The nLab - the (n-)category as a "grand narrative" in mathematics ...
A category is simply a collection of objects and morphisms. In some categories, morphisms represent functions, but in others, they do not.
Structured group cohomology (topological groups and Lie groups). If the groups in question are not plain groups (group objects internal to Set) ...
category theory - what is an ∞-group? - Mathematics Stack Exchange
I was reading on nLab and I found the term infinity group. The definition is awfully abstract: An ∞-group is a group object in ∞Grpd.
The Group With No Elements | The n-Category Café
It goes like this. A group is the same as a nonempty set with an associative binary operation ⋅ : G × ...
CMC Europe NLab Short Course - CASSS
The Netherlands Area Biotech (NLab) Discussion Group is the first CASSS discussion group located outside the US and is intended to enable the local area ...
1. Idea. The forgetful functor U U from abelian groups to commutative monoids has a left adjoint G G . This is called group completion. A ...
Why study simplicial homotopy groups? - MathOverflow
To compute the homotopy groups of a simplicial set X, you need to be able to construct a weak equivalence X→Y where Y is a Kan complex, ...
In mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways. A groupoid can be ...
The functor μ : = 𝔾 m \mu:=\mathbb{G}_m is a group scheme given by 𝔾 m ( S ) = Γ ( S , 𝒪 S ) × \mathbb{G}_m(S)=\Gamma(S, \mathcal{O}_S)^\times .
Isn't the quantomorphism group really just the "WKB ... - MathOverflow
However, at higher order, especially in interacting theories, the groups will start to diverge. In this sense, the nLab definition of the ...
... nlab/show/internal+logic). It's far from perfect, but ... group as a group object in that internal category. Note that in this ...