Classical groups
Finite groups
Group schemes
Topological groups
Lie groups
Super-Lie groups
Higher groups
Cohomology and Extensions
Related concepts
Background
Basic concepts
equivalences in/of -categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
An ∞-group is a group object in ∞Grpd.
Equivalently (by the delooping hypothesis) it is a pointed connected -groupoid.
Under the identification of ∞Grpd with Top this is known as a grouplike -space, for instance.
An -Lie group is accordingly a group object in ∞-Lie groupoids. And so on.
For details see groupoid object in an (∞,1)-category.
By
-group, braided ∞-group
free infinity-group type?
(For more see also the references at infinity-action.)
A standard textbook reference on -groups in the classical model structure on simplicial sets is
Group objects in (infinity,1)-categories are the topic of
Model category presentations of group(oid) objects in by groupoidal complete Segal spaces are discussed in
Adding inverses to diagrams encoding algebraic structures, Homology, Homotopy and Applications 10 (2008), no. 2, 149–174. (arXiv:0610291)
Adding inverses to diagrams II: Invertible homotopy theories are spaces, Homology, Homotopy and Applications, Vol. 10 (2008), No. 2, pp.175-193. (web, arXiv:0710.2254)
Discussion from the point of view of category objects in an (∞,1)-category is in
The homotopy theory of -groups that are n-connected and r-truncated for is discussed in
/S0022-4049(98)00143-1“>doi:10.1016/S0022-4049(98)00143-1</a>)
Discussion of aspects of ordinary group theory in relation to -group theory:
Discussion of -groups in homotopy type theory:
Last revised on January 24, 2023 at 17:00:02. See the history of this page for a list of all contributions to it.