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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 11th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI reworked [[A-infinity algebra]] so as to apply to algebras over any $A_\infty$-operad in any ambient category. So I created subsections "In chain complexes", "In topological spaces". I think if we speak generally of "algebra over an operad" then we should also speak generally of "$A_\infty$-algebra" even if the enriching category is not chain complexes. Otherwise it will become a mess. But I did link to [[A-infinity space]].

   I reworked A-infinity algebra so as to apply to algebras over any $A_\infty$-operad in any ambient category. So I created subsections “In chain complexes”, “In topological spaces”.

   I think if we speak generally of “algebra over an operad” then we should also speak generally of “$A_\infty$-algebra” even if the enriching category is not chain complexes. Otherwise it will become a mess. But I did link to A-infinity space.

2. • CommentRowNumber2.
   • CommentAuthorzskoda
   • CommentTimeNov 11th 2010
   • PermaLink
   Author: zskoda
   Format: MarkdownItexThere is one thing which should be once taken care of. The intuitive idea that d^2 = 0 and d is a sum of terms which correspond to various levels of asssociativity in practice is realized in two different conventioins/variants -- one in which components are denotes with $b_n$ and another in which it is denoted $m_n$. The things are more or less proportional up to minus sign things, but one should be aware always which of the two variants one is using.

   There is one thing which should be once taken care of. The intuitive idea that d^2 = 0 and d is a sum of terms which correspond to various levels of asssociativity in practice is realized in two different conventioins/variants – one in which components are denotes with $b_n$ and another in which it is denoted $m_n$. The things are more or less proportional up to minus sign things, but one should be aware always which of the two variants one is using.