equivalences in/of -categories
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
(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:
Ulrik Buchholtz, Floris van Doorn, Egbert Rijke, Higher Groups in Homotopy Type Theory, LICS ‘18: Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science (arXiv:1802.04315, doi:10.1145/3209108.3209150)
Ulrik Buchholtz, Notes on higher groups and projective spaces, 2016 (pdf)
Marc Bezem, Ulrik Buchholtz, Pierre Cagne, Bjørn Ian Dundas, Daniel R. Grayson: Section 4.6 of: Symmetry (2021) pdf
Last revised on June 24, 2022 at 12:55:00. See the history of this page for a list of all contributions to it.