https://github.com/jozefg/secret-notes

Containing small notes which aren't original or noteworthy, but which I don't want to lose.
https://github.com/jozefg/secret-notes

Last synced: 2 months ago
JSON representation

Containing small notes which aren't original or noteworthy, but which I don't want to lose.

• Host: GitHub
• URL: https://github.com/jozefg/secret-notes
• Owner: jozefg
• Created: 2020-07-08T21:23:32.000Z (almost 5 years ago)
• Default Branch: master
• Last Pushed: 2020-09-16T11:01:50.000Z (over 4 years ago)
• Last Synced: 2025-01-28T16:34:34.949Z (4 months ago)
• Language: TeX
• Homepage:
• Size: 81.1 KB
• Stars: 4
• Watchers: 3
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

Awesome Lists containing this project

README

        
## secret notes

The secrecy is marginal at best.

 - `right-adjoint-to-diagonal.tex`

 A simple and self-contained proof that the right adjoint to the diagonal is the limit functor.

 - `subobject.tex`

 An explicit construction of the subobject classifier in a glued topos.

 - `maps-into-quotients-of-colimits.tex`

 A proof that all monomorphism `PSH(C)` are generated by pushouts, retracts, and transfinite

 compositions of subobjects of quotients of representables.

 - `accessibility-topoi-and-gluing.tex`

 Random facts about accessible categories (such as raising the index of accessibility) and a proof

 that the glued category is accessible if the functor is itself accessible.

 - `invertibility-hypothesis-for-sset.tex`

 A proof of the invertibility hypothesis for simplicial categories (an instance of coherence by

 cofibrant replacement!).

 - `product-of-topoi.tex`

 A construction of the product of Grothendieck topoi as well as the corresponding tensor product on

 locally presentable categories.

 - `affine-structure-sheaf.tex`

  A construction of the structure sheaf on `Spec A`, detailing proving the gluing and restriction

  properties and extending the sheaf from a basis to the full topology.