homotopy theory, (∞,1)-category theory, homotopy type theory
flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed…
models: topological, simplicial, localic, …
see also algebraic topology
Introductions
Definitions
Paths and cylinders
Homotopy groups
Basic facts
Theorems
For $G$ a group, there is a pointed connected groupoid $(G \rightrightarrows \ast)$ with
a single object,
composition the group operation in $G$.
This may be understood as the “delooping” of $G$ in the ambient (infinity,1)-topos, and is, as such, naturally denoted $\mathbf{B}G$.
a skeletal groupoid is a disjoint union of delooping groupoids
For more see at
Last revised on May 12, 2023 at 07:32:08. See the history of this page for a list of all contributions to it.