nLab
higher structure

Contents

Context

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Homotopy theory

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

Contents

Idea

The term higher structure (as used in numerous conference titles in recent years, e.g. CGX 11, BBM 16, SBBM 18, JSSW 18 and by a journal HSJ) has come to mean essentially what elsewhere was and is called categorified mathematical structure or mathematical structure in higher category theory, or, more specifically, mathematical structure in (∞,1)-category theory, hence mathematical structure in homotopy theory (higher algebra/homotopical algebra, higher geometry/derived geometry, etc.).

For example, L-∞ algebras, which are Lie algebra objects in the (∞,1)-category of chain complexes, would be a core topic in higher structures in Lie theory (elsewhere: ∞-Lie theory).

References

General exposition:

Discussion in string theory/M-theory:

Conferences and proceedings:

Journals:

Created on August 8, 2020 at 13:43:03. See the history of this page for a list of all contributions to it.