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Table of Contents
Cover
Title page
Contents
Preface
Examples of geodesic ghor algebras on hyperbolic surfaces
1. Introduction
2. Ghor algebras: Background and main results
3. Examples
References
Feynman categories and representation theory
Introduction
1. Representations from a categorical viewpoint
2. Feynman categories
3. Constructions and examples
4. Modules and enriched Feynman categories
5. Bar, co-bar, Feynman transforms, &
master equations
6. W-construction and cubical structures
7. Outlook
Appendix A. Graph glossary and graphical Feynman categories
Appendix B. Graph description of ⁺, ^{+ } and ^{ }
Appendix C. Double categories, 2-categories and monoidal categories
Appendix D. Model structures
Acknowledgments
References
Preprojective roots and graph monoids of Coxeter groups
Introduction
1. Graph monoid
2. Preprojective roots
3. Preprojective roots and finite Coxeter groups
4. Reduced -admissible words
References
Approximable triangulated categories
1. Introduction
2. Background
3. Approximability-the intuition, which comes from ( )
4. Measuring the complexity of an object
5. The formal definition of approximability
6. The main theorems
7. More about the strong generation of \dperf and ^{ }_{ }( )
8. More about finite -linear functors :\big[\dperf \big]^{ }⟶\Mod and ̃ : ^{ }_{ }( )⟶\Mod
9. The categories \dperf and ^{ }_{ }( ) determine each other
Appendix A. Some dumb maps in _{}ℭ^{ℭ'}( ), and the proof that the third map of the triangle is a cochain map
Appendix B. The assumption that the short exact sequences of cochain complexes are degreewise split is harmless
Appendix C. Translating the approach to derived categories we presented here to the more standard one in the literature.
Acknowledgments
References
Methods of constructive category theory
Introduction
1. Category constructors
1.1. Computable categories
1.2. \Ab-categories
1.3. Additive closure
1.4. Homomorphism structures
1.5. Freyd category
1.6. Computing with Freyd categories
1.6.1. Equality of morphisms
1.6.2. Cokernels
1.6.3. Kernels
1.6.4. The abelian case
1.6.5. Homomorphisms
1.7. Computing natural transformations
2. Constructive diagram chases
2.1. Additive relations
2.2. Category of generalized morphisms
2.3. Computation rules
2.4. Cohomology
2.5. Snake lemma
2.6. Generalized homomorphism theorem
2.7. Computing spectral sequences
References
The HRS tilting process and Grothendieck hearts of t-structures
1. Introduction
2. Preliminaries
3. Projective and injective objects in the heart. Quasi-(co)tilting torsion pairs
4. When is the heart of a torsion pair a Grothendieck category?
5. Beyond the HRS case: Some recent results
Acknowledgments
References
Back Cover.
Title page
Contents
Preface
Examples of geodesic ghor algebras on hyperbolic surfaces
1. Introduction
2. Ghor algebras: Background and main results
3. Examples
References
Feynman categories and representation theory
Introduction
1. Representations from a categorical viewpoint
2. Feynman categories
3. Constructions and examples
4. Modules and enriched Feynman categories
5. Bar, co-bar, Feynman transforms, &
master equations
6. W-construction and cubical structures
7. Outlook
Appendix A. Graph glossary and graphical Feynman categories
Appendix B. Graph description of ⁺, ^{+ } and ^{ }
Appendix C. Double categories, 2-categories and monoidal categories
Appendix D. Model structures
Acknowledgments
References
Preprojective roots and graph monoids of Coxeter groups
Introduction
1. Graph monoid
2. Preprojective roots
3. Preprojective roots and finite Coxeter groups
4. Reduced -admissible words
References
Approximable triangulated categories
1. Introduction
2. Background
3. Approximability-the intuition, which comes from ( )
4. Measuring the complexity of an object
5. The formal definition of approximability
6. The main theorems
7. More about the strong generation of \dperf and ^{ }_{ }( )
8. More about finite -linear functors :\big[\dperf \big]^{ }⟶\Mod and ̃ : ^{ }_{ }( )⟶\Mod
9. The categories \dperf and ^{ }_{ }( ) determine each other
Appendix A. Some dumb maps in _{}ℭ^{ℭ'}( ), and the proof that the third map of the triangle is a cochain map
Appendix B. The assumption that the short exact sequences of cochain complexes are degreewise split is harmless
Appendix C. Translating the approach to derived categories we presented here to the more standard one in the literature.
Acknowledgments
References
Methods of constructive category theory
Introduction
1. Category constructors
1.1. Computable categories
1.2. \Ab-categories
1.3. Additive closure
1.4. Homomorphism structures
1.5. Freyd category
1.6. Computing with Freyd categories
1.6.1. Equality of morphisms
1.6.2. Cokernels
1.6.3. Kernels
1.6.4. The abelian case
1.6.5. Homomorphisms
1.7. Computing natural transformations
2. Constructive diagram chases
2.1. Additive relations
2.2. Category of generalized morphisms
2.3. Computation rules
2.4. Cohomology
2.5. Snake lemma
2.6. Generalized homomorphism theorem
2.7. Computing spectral sequences
References
The HRS tilting process and Grothendieck hearts of t-structures
1. Introduction
2. Preliminaries
3. Projective and injective objects in the heart. Quasi-(co)tilting torsion pairs
4. When is the heart of a torsion pair a Grothendieck category?
5. Beyond the HRS case: Some recent results
Acknowledgments
References
Back Cover.