nLab
Model Categories
Context
Model category theory
model category, model -category
Definitions
Morphisms
Universal constructions
Refinements
Producing new model structures
Presentation of -categories
Model structures
for -groupoids
for ∞-groupoids
for equivariant -groupoids
for rational -groupoids
for rational equivariant -groupoids
for -groupoids
for -groups
for -algebras
general -algebras
specific -algebras
for stable/spectrum objects
for -categories
for stable -categories
for -operads
for -categories
for -sheaves / -stacks
There is the textbook
on model categories and the homotopy theory modeled by them.
Preface
Chapter 1. Model categories
1.1. The definition of a model category
1.2. The homotopy category
1.3. Quillen functors and derived functors
1.3.1. Quillen functors
1.3.2. Derived functors and naturality
1.3.3. Quillen equivalences
1.4. 2-categories and pseudo-2-functors
Chapter 2. Examples
2.1. Cofibrantly generated model categories
2.1.1. Ordinals, cardinals, and transfinite compositions
2.1.2. Relative I-cell complexes and the small object argument
2.1.3. Cofibrantly generated model categories
2.2. The stable category of modules
2.3. Chain complexes of modules over a ring
2.4. Topological spaces
2.5. Chain complexes of comodules over a Hopf algebra
2.5.1. The category of B-comodules
2.5.2. Weak equivalences
2.5.3. The model structure
Chapter 3. Simplicial sets
3.1. Simplicial sets
3.2. The model structure on simplicial sets
3.3. Anodyne extensions
3.4. Homotopy groups
3.5. Minimal fibrations
3.6. Fibrations and geometric realization
Chapter 4. Monoidal model categories
4.1. Closed monoidal categories and closed modules
4.2. Monoidal model categories and modules over them
4.3. The homotopy category of a monoidal model category
Chapter 5. Framings
5.1. Diagram categories
5.2. Diagrams over Reedy categories and framings
5.3. A lemma about bisimplicial sets
5.4. Function complexes
5.5. Associativity
5.6. Naturality
5.7. Framings on pointed model categories
Chapter 6. Pointed model categories
6.1. The suspension and loop functors
6.2. Cofiber and fiber sequences
6.3. Properties of cofiber and fiber sequences
6.4. Naturality of cofiber sequences
6.5. Pre-triangulated categories
6.6. Pointed monoidal model categories
Chapter 7. Stable model categories and triangulated categories
7.1. Triangulated categories
7.2. Stable homotopy categories
7.3. Weak generators
7.4. Finitely generated model categories
Chapter 8. Vistas
Bibliography
Index
Last revised on April 18, 2023 at 16:33:58.
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