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Taylor towers for functors of additive categories. (English) Zbl 0929.18007
Let \(F : {\mathcal A}\to {\mathcal B}\) be a functor of additive categories.
The authors modify MacLane’s \(Q\)-construction to generalize Dold-Puppe’s construction [A. Dold and D. Puppe, Ann. Inst. Fourier 11, 201-312 (1961; Zbl 0098.36005)] and develop a tower of functors and natural transformations \[ \cdots\to P_nF\to P_{n-1}F\to\cdots\to P_1F\to P_0F=F(0) \] for the functor \(F\). It is proved that \(P_nF\) is a homologically degree \(n\) functor and universal among such functors and with natural transformations from \(F\).
Conditions under which this tower is equivalent with Goodwillie’s tower [T. G. Goodwillie, \(K\)-Theory 5, No. 4, 295-332 (1992; Zbl 0776.55008)] are established.

18G10 Resolutions; derived functors (category-theoretic aspects)
18E25 Derived functors and satellites (MSC2010)
55P65 Homotopy functors in algebraic topology
55U99 Applied homological algebra and category theory in algebraic topology
Full Text: DOI
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