• Tags
  • #homotopy/stable-homotopy #higher-algebra/infty-cats
• Refs:
  • https://nilesjohnson.net/drafts/Johnson_Yau_ring_categories.pdf#page=1057
  • attachments/SimplicialHomotopyLectures.pdf
  • Chapter 3 https://mandal.ku.edu/M996QuillenKTheory/0TheKBooK.pdf
  • http://pi.math.cornell.edu/~web7400/7400-notes_05_10_15.pdf
  • attachments/Gyan_Singh_sSet.pdf
• Links:
  • Model structure on sSet
  • nerve

simplicial set

Notes

• \({\mathsf{sSet}}= {\mathsf{Fun}}({ {\Delta}^{\operatorname{op}}}, {\mathsf{Set}}) = \underset{ \mathsf{pre} } {\mathsf{Sh} }(\Delta, {\mathsf{Set}})\)

• Functors \(\Delta^{\operatorname{op}}\to{\mathsf{Set}}\) where \(\Delta \leq {\mathsf{FinSet}}\) are totally ordered finite sets \([n] = \left\{{0, 1, 2, \cdots, n}\right\}\) for all \(n\geq 0\), with order-preserving set-maps.

  • I.e. presheaf on \(\Delta\).
  • Morphisms are natural transformations.

• Used to define quasicategory.

• The “dual” of geometric realization is totalization? #todo/questions

Pasted image 20211108235121.png

Mapping objects

Joins

Op

Constant objects

Model structure