Author Description

A Detailed Treatment Of Mackey Functors And Homotopical Applications In The Broader Context Of Enriched Diagram Categories, Suitable For Graduate Students Or Researchers With An Interest In Category Theory, Equivariant Homotopy Theory, Or Related Fields. A Self-contained Reference, With Complete Definitions And Full Proofs For Non-expert Readers-- Cover -- Series Page -- Title Page -- Imprints Page -- Dedication -- Contents -- List Of Main Facts -- List Of Notations -- Preface -- 1 Motivations From Equivariant Topology -- 1.1 Equivariant Spaces And Presheaves On The Orbit Category -- 1.2 The Burnside Category And Abelian G-mackey Functors -- 1.3 Equivariant Spectra And Presheaves On The Burnside 2-category -- 1.4 Stable Model Categories As Spectral Presheaf Categories -- Part 1 Background On Multicategories And K-theory Functors -- 2 Categorically Enriched Multicategories -- 2.1 Multicategories -- 2.2 Pointed Multicategories -- 2.3 M1-modules -- 2.4 Permutative Categories -- 3 Infinite Loop Space Machines -- 3.1 Homotopy Theories Via Complete Segal Spaces -- 3.2 Category Of Pointed Diagrams -- 3.3 Γ-objects -- 3.4 G[sub(*)]-objects -- 3.5 Segal And Elmendorf-mandell K-theory -- 4 Homotopy Theory Of Multicategories -- 4.1 Free Permutative Categories -- 4.2 Free Permutative Category As A Left 2-adjoint -- 4.3 Componentwise Right Adjoint Of The Counit -- 4.4 Free Permutative Category As A Nonsymmetric Cat-multifunctor -- 4.5 Homotopy Equivalences Between Multicategories And Permutative Categories -- Part 2 Homotopy Theory Of Pointed Multicategories, M1-modules, And Permutative Categories -- 5 Pointed Multicategories And M1-modulesmodel All Connective Spectra -- 5.1 Pointed Free Permutative Categories -- 5.2 Relating Unpointed And Pointed Free Permutative Categories -- 5.3 Pointed Free Permutative Category As A Left 2-adjoint -- 5.4 Free Permutative Categories Of M1-modules -- 5.5 Examples Of Pointed Free Permutative Categories -- 5.6 Componentwise Right Adjoint Of The