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(infinity,1)-module

Idea

The notion of $(\mathrm{\infty },1)$-module over an monoid object in an (∞,1)-category (for instance an A-∞ ring or E-∞ ring) is the generalization to (stable)homotopy theory of the notion of module over a ring.

Definition

See at module over an algebra over an (∞,1)-operad.

Examples

• in the stable (∞,1)-category of spectra: module spectrum over an ring spectrum

Related concepts

• action, ∞-action

• module, $(\mathrm{\infty },1)$-module

  • tensor product of ∞-modules

  • 2-module

• bimodule

  (∞,1)-bimodule

• (∞,n)-module

• representation, ∞-representation

References

Modues over algebras over an arbitrary (∞,1)-operad are discussed in section 3.3 of

• Jacob Lurie, Higher Algebra

Modules specifically over A-∞ algebras are discussed in section 4.2 there.