Homological Interpretation of Extensions and Biextensions of Complexes
نویسنده
چکیده
Let T be a topos. Let Ki = [Ai ui → Bi] (for i = 1, 2, 3) be a complex of commutative groups of T with Ai in degree 1 and Bi in degree 0. We define the geometrical notions of extension of K1 by K3 and of biextension of (K1, K2) by K3. These two notions generalize to complexes with two entries the classical notions of extension and biextension of commutative groups of T. We then apply the geometrical-homological principle of Grothendieck in order to compute the homological interpretation of extensions and biextensions of complexes.
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