group theory
general linear group
unitary group
orthogonal group
symplectic group
finite group
symmetric group, cyclic group, braid group
classification of finite simple groups
sporadic finite simple groups
topological group
compact topological group, locally compact topological group
maximal compact subgroup
string group
Lie group
compact Lie group
Kac-Moody group
super Lie group
super Euclidean group
2-group
n-group
∞-group
simplicial group
crossed complex
k-tuply groupal n-groupoid
spectrum
circle n-group, string 2-group, fivebrane Lie 6-group
group cohomology
group extension,
∞-group extension, Ext-group
Edit this sidebar
higher algebra
universal algebra
algebraic theory / 2-algebraic theory / (∞,1)-algebraic theory
monad / (∞,1)-monad
operad / (∞,1)-operad
algebra over a monad
∞-algebra over an (∞,1)-monad
algebra over an algebraic theory
∞-algebra over an (∞,1)-algebraic theory
algebra over an operad
∞-algebra over an (∞,1)-operad
action, ∞-action
representation, ∞-representation
module, ∞-module
associated bundle, associated ∞-bundle
monoidal (∞,1)-category
symmetric monoidal (∞,1)-category
monoid in an (∞,1)-category
commutative monoid in an (∞,1)-category
symmetric monoidal (∞,1)-category of spectra
smash product of spectra
symmetric monoidal smash product of spectra
ring spectrum, module spectrum, algebra spectrum
A-∞ algebra
C-∞ algebra
E-∞ ring, E-∞ algebra
∞-module, (∞,1)-module bundle
multiplicative cohomology theory
L-∞ algebra
model structure on simplicial T-algebras / homotopy T-algebra
model structure on operads
model structure on algebras over an operad
Isbell duality
derived geometry
Deligne conjecture
delooping hypothesis
monoidal Dold-Kan correspondence
An ordinary group is either an abelian group or not. For an ∞-group there is an infinite tower of notions ranging from completely non-abelian to completely abelian.
Section 5 of