Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
  
  
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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 -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 “-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 and another in which it is denoted . 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.