Calculus II: Analytic functors

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Abstract
Homotopy functors (for example, from spaces to spaces) are called analytic if, when evaluated on certain n-cubical diagrams, they satisfy certain connectivity estimates. Tools for verifying these estimates include certain generalizations of the triad connectivity theorem. Waldhausen's functor A is analytic. Analyticity has strong consequences, when combined with the concept ‘derivative of a homotopy functor’ that was introduced in the previous article in this series. In particular, any analytic functor with derivative zero is, in a sense, locally constant.

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