nLab
nonunital Ek-algebra

Contents

Idea

The nonunital variant of Ek-algebra, hence the generalization of the concept of nonunital ring from algebra to higher algebra.

Properties

Relation to augmented 𝔼 k\mathbb{E}_k-algebra

Nonunital 𝔼 k\mathbb{E}_k-algebras are equivalent to unital 𝔼 k\mathbb{E}_k-algebras sliced over the free 𝔼 k\mathbb{E}_k-algebra on a single generator.

In particular nonunital E-∞ algebras are equivalent to unital E E_\infty-algebras sliced over the sphere spectrum:

E Ring nuE Ring /𝕊, E_\infty Ring^{nu} \simeq E_\infty Ring_{/\mathbb{S}} \,,

where the map from right to left is given by 𝔼 k\mathbb{E}_k-unitalization and the converse by forming augmentation ideals.

(Lurie, prop. 5.2.3.15)

References

Last revised on August 22, 2014 at 07:09:05. See the history of this page for a list of all contributions to it.