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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.

##### MSC:
 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
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