20/09/05 16:42:58.23 YJxrx+O5.net
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つづき
上記”Yoneda pairing”にリンクが張ってあって、下記に飛ぶ
URLﾘﾝｸ(en.wikipedia.org)
Yoneda product
(抜粋)
In algebra, the Yoneda product (named after Nobuo Yoneda) is the pairing between Ext groups of modules:
Ext^n (M,N)◯x Ext^{m}(L,M) → Ext^{n+m}(L,N)
induced by
Hom (N,M)◯x Hom (M,L) → Hom (N,L),f◯x g → g ・ f.
Specifically, for an element xi ∈ Ext^n (M,N), thought of as an extension
xi :0 → N → E_{0} → ・・・ → E_{n-1} → M → 0,
and similarly
ρ :0 → M → F_{0} → ・・・ → F_{m-1} → L → 0 ∈ Ext^{m}(L,M)
we form the Yoneda (cup) product
xi smile ρ :0 → N → E_{0} → ・・・ → E_{n-1} → F_{0} → ・・・ → F_{m-1} → L → 0 ∈ Ext^{m+n}(L,N).
Note that the middle map E_{n-1} → F_{0}} E_{n-1} → F_{0}} factors through the given maps to M.
We extend this definition to include m,n=0} m,n=0} using the usual functoriality of the Ext^{*}(_,_) groups.
Contents
1 Applications
1.1 Ext Algebras
1.2 Grothendieck duality
1.3 Deformation theory
2 See Also
3 References
4 External links
つづく