∞-Lie theory (higher geometry)
A path -groupoid of a smooth space (or generalized smooth space) is a diffeological n-groupoid which is
a generalization of the path groupoid to higher categorical dimension
a truncation of sorts of an path ∞-groupoid of .
Its j-morphisms are given by (possibly equivalence classes of) -dimensional smooth paths in , i.e. usually smooth maps . Composition is by gluing of such maps.
See path groupoid.
Definitions of path 2-groupoids as strict 2-groupoids internal to diffeological spaces appear (at least) in
John Baez, Urs Schreiber, Higher gauge theory (arXiv)
Urs Schreiber, Konrad Waldorf, Smooth functors vs. differential forms (arXiv)
João Faria Martins, Roger Picken, On 2-dimensional holonomy (arXiv)
A realization of the path 3-groupoid as a Gray-groupoid internal to diffeological spaces appears in
Last revised on February 3, 2021 at 17:28:36. See the history of this page for a list of all contributions to it.