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Download PDF by Jaume Aguadé, Carles Broto, Laia Saumell (auth.), Gregory: Categorical Decomposition Techniques in Algebraic Topology:

0 after composing with F. References [BPj S. Betley, T. Pirashvili. Stable K-theory as a derived functor. J. Pure and Applied Algebra 96 (1994) 245-258. [BSj S. Betley, J. Slominska. (Lm, Lien) by the homology theory of the category of functors.

Then the natural map Q -7 P 0 F3 induces an isomorphism Ext'F(P 0 F3, Jd) -7 Ext'F(Q, Jd) Proof. Let K be the kernel of P 0 F2 -7 Po F3. 3 Ext'F(K/PoFI,Id) = O. Hence the embedding PoFI -7 K induces an isomorphism Ext'F(K,Id) -7 Ext'F(P 0 FI,Jd). This proves our lemma by a long exact sequence argument and 5-lemma. 5 are formulated for short exact sequences of functors. We will use them usually for long exact sequences so the corollary below is formulated here for the readers convenience. 6. Corollary.

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