非代数的高次圏論の基本概念

ビデオとテキスト〈解説論文〉

今は順不同だが整列する。

  1. simplicial set https://ncatlab.org/nlab/show/simplicial+set
  2. simplicial object https://ncatlab.org/nlab/show/simplicial+object
  3. simplicial space https://ncatlab.org/nlab/show/simplicial+topological+space
  4. simplicial category → simplicially enriched category 曖昧性は https://ncatlab.org/nlab/show/simplicial+category
  5. Nerve construction https://ncatlab.org/nlab/show/nerve
  6. Segal condition https://ncatlab.org/nlab/show/Segal+condition
  7. simplicially enriched category https://ncatlab.org/nlab/show/simplicially+enriched+category
  8. model category https://ncatlab.org/nlab/show/model+category
  9. weak factorization system https://ncatlab.org/nlab/show/weak+factorization+system
  10. homotopical category https://ncatlab.org/nlab/show/homotopical+category
  11. category with weak equivalences https://ncatlab.org/nlab/show/category+with+weak+equivalences
  12. relative category https://ncatlab.org/nlab/show/relative+category
  13. Quillen pair/adjunction https://ncatlab.org/nlab/show/Quillen+adjunction
  14. Quillen equivalnece https://ncatlab.org/nlab/show/Quillen+equivalence
  15. Segal map https://ncatlab.org/nlab/show/Segal+map
  16. Segal category https://ncatlab.org/nlab/show/Segal+category
  17. simplicial localization https://ncatlab.org/nlab/show/simplicial+localization
  18. fibrant-cofibrant replacement https://ncatlab.org/nlab/show/fibrant+replacement
  19. Dwyer-Kan equivalence https://ncatlab.org/nlab/show/model+structure+on+sSet-categories
  20. Reedy category https://ncatlab.org/nlab/show/Reedy+category
  21. Reedy model structure https://ncatlab.org/nlab/show/Reedy+model+structure
  22. Segal space https://ncatlab.org/nlab/show/Segal+space
  23. inner horn https://ncatlab.org/nlab/show/horn
  24. fundamental category https://ncatlab.org/nlab/show/fundamental+category
  25. fibrant object https://ncatlab.org/nlab/show/fibrant+object
  26. Rezk's model structure https://ncatlab.org/nlab/show/model+structure+for+complete+Segal+spaces
  27. discretization functor ?
  28. rigidification functor https://pages.uoregon.edu/ddugger/rigidqc.pdf