Skip to main content

All Questions

Filter by
Sorted by
Tagged with
7 votes
1 answer
474 views

Explicit chain homotopy for the Alexander-Whitney, Eilenberg-Zilber pair

Let $A$ and $B$ be simplicial abelian groups, and let $N_\ast(-)$ denote the normalized chain complex functor. Let $$AW_{A,B}\colon N_\ast(A\otimes B) \longrightarrow N_\ast(A)\otimes N_\ast(B)$$ and ...
User371's user avatar
  • 517
12 votes
0 answers
917 views

Are the Alexander-Whitney and Eilenberg-Zilber maps homotopy inverse in arbitrary abelian categories?

Let $\mathcal{A}$ be a monoidal abelian category. Let $A$ and $B$ be simplicial objects in $\mathcal{A}$, and let $N_\ast(-)$ denote the normalized chain complex functor. Let $$AW_{A,B}\colon N_\ast(...
Richard Hepworth's user avatar