Enriched functor categories for functor calculus (original) (raw)

In this paper we present background results in enriched category theory and enriched model category theory necessary for developing model categories of enriched functors suitable for doing functor calculus. Contents 1. Introduction 1 Organization of the paper 3 2. Enriched categories 4 3. The enriched Yoneda Lemma 8 4. Enriched functor categories 11 5. Enriched model categories 17 6. Homotopy limits, homotopy colimits, and the evaluated cotensor in simplicial model categories 20 7. An application to functor calculus 23 7.1. A simplicial representable replacement for Goodwillie calculus 24 7.2. A simplicial representable replacement for discrete calculus 25 7.3. Simplicial functors 28 References 30