group theory in nLab
Eugene P. Wigner: Group theory: And its application to the quantum mechanics of atomic spectra, 5, Academic Press (1959)
A group is an algebraic structure consisting of a set G G and a binary operation ⋆ \star that satisfies the group axioms, being:.
combinatorial group theory in nLab
nLab combinatorial group theory ... Combinatorial group theory is an approach to the theory of discrete groups based on presentations of groups, ...
group theory - contents in nLab
nLab group theory - contents · group, ∞-group · group object, group object in an (∞,1)-category · abelian group, spectrum · super abelian group ...
geometric group theory in nLab
Geometric group theory studies groups by equipping them with a metric and thus regarding them as metric spaces.
The nLab is a wiki for research-level notes, expositions and collaborative work, including original research, in mathematics, physics, and philosophy, ...
Motivation for the nLab's definition of cohomology?
It can also be described as trying to make higher homotopy theory look more like that of the fundamental group, and so nonabelian (in this book ...
The theory of group objects is an example of a Lawvere theory. 5. Related concepts. monoid, monoid object, monoid object in an (∞,1)-category · group, group ...
The nLab - the (n-)category as a "grand narrative" in mathematics ...
"Higher category theory studies the generalization of ∞-groupoids – and hence, via the homotopy hypothesis, of topological spaces – to that of ...
For topological groups ... Proposition 2.2. Let G G be a topological group, and X X be a set with a G G action μ : G × X → X \mu: G \times X \to X ...
Being Tentative on nLab | The n-Category Café
Whitehead's theorem says that if a map between connected CW complexes induces isomorphisms of all homotopy groups, then the map is a homotopy ...
What non-categorical applications are there of homotopical algebra?
... nLab.) More and more lately I have been unexpectedly running into ... For example in geometric group theory you here people say that a ...
From the nLab to the HoTT Book - Sandiego
• ZFC is synthetic set theory: basic objects are sets. • Ordinary type theory is hardly different in this. • HoTT/UF is synthetic homotopy theory. Page 34. The ...
A presentation of a group, G G , is a coequalizer diagram F R ⇉ F X ↠ G F R \rightrightarrows F X \twoheadrightarrow G , where F X F X is the ...
Idea Of Ends On nLab - category theory - Math Stack Exchange
First, every group G can be considered as a special kind of category. This category, often notated BG consists of a single object ...
Is nLab a good source? : r/math - Reddit
nLab presents category theory (and mathematics as a whole) from a ... group of a torus, which were incredibly awkward (since that's a ...
In mathematics, especially in category theory and homotopy theory, a groupoid generalises the notion of group in several equivalent ways. A groupoid can be ...
People had been using groups (implicitly or otherwise) long before the modern foundations of model theory were established with the theorems of ...
A group blog on math, physics and philosophy ... A satire generator making fun of the nLab, a wiki for higher mathematics and category theory.
In the late 1920s, Eugene Wigner and Hermann Weyl highlighted the role that group theory and representation theory play in the analysis of quantum mechanics.