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
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
Discussion in homotopy type theory is in
For more see the references at infinity-action.
Last revised on October 31, 2020 at 08:10:05. See the history of this page for a list of all contributions to it.