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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJun 19th 2013
• CommentRowNumber2.
• CommentAuthorjim_stasheff
• CommentTimeJun 20th 2013
The title is a bit misleading since you have something much more spectral in mind. Some misprints in the references.
• CommentRowNumber3.
• CommentAuthorGuest
• CommentTimeJun 20th 2013
(I'm just testing something ... Andrew)
• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJun 20th 2013
• (edited Jun 20th 2013)

Thansk, Jim.

I have now added a warning remark here about a possible simplicial meaning of augmentation that one might think of.

Also I have fixed some misprints. (Possiby I did introduce new misprints though… ;-)

• CommentRowNumber5.
• CommentAuthorjim_stasheff
• CommentTimeJun 21st 2013
Not sure I made my point clear; there is the notion of augmentation for an Aoo-algebra pure and simple
• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJun 21st 2013

there is the notion of augmentation for an Aoo-algebra pure and simple

Hm, you mean a notion different from the pure and simple “equipped with a map to the base $\infty$-ring”, as in the entry?

Maybe you just want me to make a distinction between on the one hand $A_\infty$-algebras in characteristic 0, hence in chain complexes and on the other the general notion of $A_\infty$-algebras in spectra? If so, I’d ask: why? The simple definition of augmentation does not depend on this.

• CommentRowNumber7.
• CommentAuthorJon Beardsley
• CommentTimeJun 22nd 2013

Haha, speaking of misprints: I know of a mathematician named Gregory Arone, but not Fregory Arone! :-)

• CommentRowNumber8.
• CommentAuthorjim_stasheff
• CommentTimeJun 22nd 2013
Urs,
I just meant without invoking $E_\infty$
• CommentRowNumber9.
• CommentAuthorjim_stasheff
• CommentTimeJun 22nd 2013
Urs, I just meant without invoking Eoo
• CommentRowNumber10.
• CommentAuthorTodd_Trimble
• CommentTimeJun 22nd 2013

Jim, in case this helps, you can render LaTeX in comments by first clicking on Markdown+Itex, where it says “Format comments as” below the comment box.

• CommentRowNumber11.
• CommentAuthorUrs
• CommentTimeJun 22nd 2013

Jim,

to the base E-∞ ring (which might be a plain commutative ring).

Does that help?

• CommentRowNumber12.
• CommentAuthorjim_stasheff
• CommentTimeJun 23rd 2013
yes, that helps
• CommentRowNumber13.
• CommentAuthorUrs
• CommentTimeAug 22nd 2014

added to the Definition-section of augmented A-infinity algebra a pointer to the very general definition 5.2.3.14 in Higher Algebra.