This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Emily Riehl is a Benjamin Peirce Fellow in the Department of Mathematics at Harvard University, Massachusetts and a National Science Foundation Mathematical Sciences Postdoctoral Research Fellow.
Inhaltsangabe
Part I. Derived Functors and Homotopy (Co)limits: 1. All concepts are Kan extensions 2. Derived functors via deformations 3. Basic concepts of enriched category theory 4. The unreasonably effective (co)bar construction 5. Homotopy limits and colimits: the theory 6. Homotopy limits and colimits: the practice Part II. Enriched Homotopy Theory: 7. Weighted limits and colimits 8. Categorical tools for homotopy (co)limit computations 9. Weighted homotopy limits and colimits 10. Derived enrichment Part III. Model Categories and Weak Factorization Systems: 11. Weak factorization systems in model categories 12. Algebraic perspectives on the small object argument 13. Enriched factorizations and enriched lifting properties 14. A brief tour of Reedy category theory Part IV. Quasi-Categories: 15. Preliminaries on quasi-categories 16. Simplicial categories and homotopy coherence 17. Isomorphisms in quasi-categories 18. A sampling of 2-categorical aspects of quasi-category theory.
Part I. Derived Functors and Homotopy (Co)limits: 1. All concepts are Kan extensions 2. Derived functors via deformations 3. Basic concepts of enriched category theory 4. The unreasonably effective (co)bar construction 5. Homotopy limits and colimits: the theory 6. Homotopy limits and colimits: the practice Part II. Enriched Homotopy Theory: 7. Weighted limits and colimits 8. Categorical tools for homotopy (co)limit computations 9. Weighted homotopy limits and colimits 10. Derived enrichment Part III. Model Categories and Weak Factorization Systems: 11. Weak factorization systems in model categories 12. Algebraic perspectives on the small object argument 13. Enriched factorizations and enriched lifting properties 14. A brief tour of Reedy category theory Part IV. Quasi-Categories: 15. Preliminaries on quasi-categories 16. Simplicial categories and homotopy coherence 17. Isomorphisms in quasi-categories 18. A sampling of 2-categorical aspects of quasi-category theory.
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