nLab
infinity-field

Context

Higher linear algebra

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 notion of A A_\infty-field is to the notion of A-∞ algebra as that of field is to associative algebra/ring.

Definition

Definition

An A-∞ ring or in fact just an H-space AA is a field if π A\pi_\bullet A is a graded field.

For instance (Lurie, lecture 24, def. 3).

Properties

For EE an \infty-field, def. , then it carries the structure of an ∞-module over the nnth Morava K-theory spectrum K(n)K(n), for some nn.

(Lurie 10, lect 25, cor 10)

This follows with the nilpotence theorem.

Examples

References

Definition 3 in

Last revised on August 20, 2014 at 23:57:09. See the history of this page for a list of all contributions to it.