Tweetovi

Blokirali ste korisnika/cu @algebraicgeome1

Jeste li sigurni da želite vidjeti te tweetove? Time nećete deblokirati korisnika/cu @algebraicgeome1

  1. Prikvačeni tweet

    There's affine line between liking homotopy theory and liking motivic homotopy theory.

    Poništi
  2. proslijedio/la je Tweet
    prije 13 sati

    I’m close to covering all of it finally. Any help... helps

    Poništi
  3. proslijedio/la je Tweet
    13. ožu 2018.

    I just want to be accepted like computers are, when they say "We're sorry, something went wrong".

    Poništi
  4. should assign the elements of C to maps X --> lim(D) and not maps from lim(D) to X... What's going on? [2/2]

    Prikaži ovu nit
    Poništi
  5. Actually I'm a bit confused now. Requiring these presheaves (call them LIM) to be representable gives a bijection between C= {Cones over a diagram with conepoint X} and Maps Iim(D) --> X. However for LIM(D) to be representable would give LIM(D)=h_lim(D), meaning that we [1/2]

    Prikaži ovu nit
    Poništi
  6. proslijedio/la je Tweet
    4. velj

    Hyped about my new book, especially considering that it's got my name in it... 🤯🤯🤯

    Prikaži ovu nit
    Poništi
  7. this gives a map lim(D) --> lim(D'). Thus lim(-) is a functor.

    Prikaži ovu nit
    Poništi
  8. We can use this to show that taking the limit is a functor: - If limits exist in C, then the presheaves LIM are all representable; - Given a map of diagrams η: D ==> D', we get a map h_lim(D) = LIM(D) ----> LIM(D') = h_lim(D'); - By the fully-faithfulness of the Yoneda embedding,

    Prikaži ovu nit
    Poništi
  9. One can then go on and cleanly show that the construction D |--> LIM(D) is functorial: Given a natural transformation η: D => D', we compose the maps in Hom_Fun(I,C)(k_X,D) with η (that is, cones over D with "cone-point" X go to cones over D' with "cone-point" X.

    Prikaži ovu nit
    Poništi
  10. And the map from lim(D) to X we send this cone to is the universal one:

    Prikaži ovu nit
    Poništi
  11. Then a cone over D is a diagram

    Prikaži ovu nit
    Poništi
  12. The map lim(D)--> X here is the universal map given in the universal property of the limit. For instance, if D is a pullback diagram of the form

    Prikaži ovu nit
    Poništi
  13. Given a diagram D:I-->C, the presheaf LIM sends X ∈ C to the set of cones over D having "cone-point" X. Asking for LIM to be representable means that there is an object lim(D) ∈ C such that there is a bijection {Cones over X} <--> {Maps lim(D) --> X}.

    Prikaži ovu nit
    Poništi
  14. TIL something really cool: Limits are defined as representing objects of certain presheaves in SGA IV.

    Prikaži ovu nit
    Poništi
  15. proslijedio/la je Tweet
    3. velj

    This is real. This is a real-life post by an anti-abortion activist. You can’t make this shit up.

    Prikaži ovu nit
    Poništi
  16. Gonna start calling Lurie's Higher Topos Theory "The Notorious H.T.T."

    Poništi
  17. proslijedio/la je Tweet
    3. velj
    Poništi
  18. proslijedio/la je Tweet
    2. velj

    in 2020 we format nested loops for what they are

    Poništi
  19. proslijedio/la je Tweet
    3. velj

    2019 was the year of me coming into my own as a woman and mathematician. This year is about flaunting it.

    Prikaži ovu nit
    Poništi
  20. proslijedio/la je Tweet
    2. velj

    Love thinking about the Grothendieck-Hatsune group

    Poništi
  21. Poništi

Čini se da učitavanje traje već neko vrijeme.

Twitter je možda preopterećen ili ima kratkotrajnih poteškoća u radu. Pokušajte ponovno ili potražite dodatne informacije u odjeljku Status Twittera.

    Možda bi vam se svidjelo i ovo:

    ·