دانلود کتاب (Co)end Calculus

فهرست مطالب :

Contents Preface 1 Dinaturality and (Co)ends 1.1 Supernaturality 1.2 (Co)ends as (Co)limits 1.3 The Fubini Rule 1.4 First Instances of (Co)ends Exercises 2 Yoneda and Kan 2.1 The Yoneda Lemma and Kan Extensions 2.2 Yoneda Lemma Using (Co)ends 2.3 Kan Extensions Using (Co)ends 2.4 A Yoneda Structure on Cat 2.5 Addendum: Relative Monads Exercises 3 Nerves and Realisations 3.1 The Classical Nerve and Realisation 3.2 Abstract Realisations and Nerves Exercises 4 Weighted (Co)limits 4.1 Weighted Limits and Colimits 4.2 Examples of Weighted Colimits 4.3 Enriched (Co)ends Exercises 5 Profunctors 5.1 The 2-Category of Profunctors 5.2 Embeddings and Adjoints 5.3 The Structure of Prof 5.4 A More Abstra ct Look at Prof 5.5 Addendum: Fourier Theory 5.6 Addendum: Tambara Theory Exercises 6 Operads 6.1 Introduction 6.2 The Convolution Product 6.3 Substitution Product and Operads 6.4 Some More Advanced Results Exercises 7 Higher Dimensional (Co)ends 7.1 2-Dimensional Coends 7.2 Coends in Homotopy Theory 7.3 (Co)ends in Quasicategories 7.4 (Co)ends in a Derivator Exercises Appendix A. Review of Category Theory A.1 Categories and Functors A.2 Natural Transformations A.3 Limits and Colimits A.4 Adjunctions A.5 The Yoneda Lemma A.6 Monoidal Categories and Monads A.7 2-Categories A.8 Higher Categories A.9 Miscellaneous Definitions Exercises Appendix B. Table of Notable Integrals References AB CD EFG HIJK LM NPR STUW Y Index