Structured chain complexes (Ex)

Show that

1. $W^{\%}(C \oplus D) \simeq W^{\%}(C) \oplus W^{\%}(D) \oplus (C \otimes D)$$<wikitex>; Show that # $W^{\%}(C \oplus D) \simeq W^{\%}(C) \oplus W^{\%}(D) \oplus (C \otimes D)$, # $W_{\%}(C \oplus D) \simeq W_{\%}(C) \oplus W_{\%}(D) \oplus (C \otimes D)$, # $\widehat{W}^{\%}(C \oplus D) \simeq \widehat{W}^{\%}(C) \oplus \widehat{W}^{\%}(D)$. </wikitex> == References== {{#RefList:}} [[Category:Exercises]] [[Category:Exercises without solution]]W^{\%}(C \oplus D) \simeq W^{\%}(C) \oplus W^{\%}(D) \oplus (C \otimes D)$,
2. $W_{\%}(C \oplus D) \simeq W_{\%}(C) \oplus W_{\%}(D) \oplus (C \otimes D)$$W_{\%}(C \oplus D) \simeq W_{\%}(C) \oplus W_{\%}(D) \oplus (C \otimes D)$,
3. $\widehat{W}^{\%}(C \oplus D) \simeq \widehat{W}^{\%}(C) \oplus \widehat{W}^{\%}(D)$$\widehat{W}^{\%}(C \oplus D) \simeq \widehat{W}^{\%}(C) \oplus \widehat{W}^{\%}(D)$.