nLab group theory




Group Theory



The study of groups.

There are many generalizations and related structures; for example the vertical categorifications of groups like 2-groups, horizontal categorifications as groupoids, groups with structure, like topological groups, Lie groups, thus also Lie groupoids, Lie infinity-groupoids; and noncommutative generalizations like quantum groups. Lie and algebraic group(oid)s have their infinitesimal precursors like formal groups, local Lie groups, tangent Lie algebras, tangent Lie algebroids etc. In the smooth context the relation between Lie groupoids and Lie algebroids is the subject of Lie theory.


Lecture notes:


in general:

in a more general context of algebra:

and in relation to applications in (quantum) physics (cf. “Gruppenpest”):

See also:

Formalization in univalent foundations of mathematics (homotopy type theory with the univalence axiom)

and implementation in Agda:

On aspects of group theory seen inside homotopy theory/ \infty -group theory:

category: group theory

Last revised on June 26, 2024 at 07:01:46. See the history of this page for a list of all contributions to it.