nLab augmented infinity-group

Idea

An ∞-group equipped with a map to a fixed base ∞-group, such as that underlying the sphere spectrum or an Eilenberg-MacLane spectrum.

Related concepts

• augmentation

• augmented algebra, augmentation ideal

• augmented A-infinity algebra

References

Discussion of ∞-groups of units of E-∞ rings as abelian ∞-groups augmented over the sphere spectrum is in

• Steffen Sagave, Spectra of units for periodic ring spectra (arXiv:1111.6731)

Augmentation over the Eilenberg-MacLane spectrum $H\mathbb{Z}$ appears in

• Gregory Arone, Kathryn Lesh, Augmented $\Gamma$-spaces, the stable rank filtration, and a $b u$-analogue of the Whitehead conjecture (pdf)