Abstract
We formulate and prove a chain rule for the derivative, in the sense of Goodwillie, of compositions of weak homotopy functors from simplicial sets to simplicial sets. The derivative spectrum of such a functor at a simplicial set can be equipped with a right action by the loop group of its domain , and a free left action by the loop group of its codomain . The derivative spectrum of a composite of such functors is then stably equivalent to the balanced smash product of the derivatives and , with respect to the two actions of the loop group of . As an application we provide a non-manifold computation of the derivative of the functor .
Citation
John R Klein. John Rognes. "A chain rule in the calculus of homotopy functors." Geom. Topol. 6 (2) 853 - 887, 2002. https://doi.org/10.2140/gt.2002.6.853
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