Posur, Sebastian: Constructive category theory and applications to equivariant sheaves. 2017
Inhalt
- Summary
- Zusammenfassung
- Contents
- Introduction
- The Cap Project
- Chapter 1. Constructive Category Theory
- 1. Preliminaries
- 2. Additive, Abelian, and Coproduct Categories
- 3. Constructing Tensor Categories
- 3.1. Bilinear Bifunctors
- 3.2. Monoidal Categories
- 3.3. Skeletal Tensor Categories
- 3.3.1. Representation Category of Finite Groups
- 3.3.2. Defining a Bifunctor
- 3.3.3. Defining an Associator
- 3.3.4. Defining a Braiding
- 3.3.5. Defining Unitors
- 3.3.6. Defining Duals
- 3.3.7. Skeletal Representation Category of Finite Groups
- 3.3.8. Graded Group Representations
- 3.3.9. Example: S3
- 3.3.10. Example: D8 and Q8
- 3.3.11. Example: Subgroup of Order 1000 of the Automorphism Group of the Horrocks-Mumford Bundle
- Chapter 2. Constructive Homological Algebra
- 1. Generalized Morphisms
- 1.1. Additive Relations
- 1.2. Categorification of Additive Relations
- 1.3. Computation Rules for Generalized Morphisms
- 1.4. Data Structures for Generalized Morphisms
- 1.5. Epi-Mono Factorizations of Generalized Morphisms
- 1.6. Attributes and Properties of Generalized Morphisms
- 1.7. Reasoning with the Canonical Objects
- 2. Diagram Chases and Spectral Sequences
- Chapter 3. Applications to Equivariant Sheaves
- 1. (Co)homological Invariants
- 2. Equivariant Modules over the Exterior Algebra
- 3. Computations with Equivariant Sheaves
- List of Figures
- Bibliography
- Index