概论

数学

发现

Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

用中文

  • 读物 书 影片 维基百科

Software


See: Krasauskas Kulikauskas

Understand the Univalence Axiom and Voevodsky's homotopy type theory in terms of my philosophical concepts.


同伦类型论 . . . Homotopy type theory


  • Relate the univalence axiom {$(A=B) \simeq (A\simeq B)$} and the Yoneda lemma

{$F(A)\cong\{\{A\rightarrow\_\}\rightarrow F(\_)\}$}.

  • Study the kinds of equivalences. Associate them to the relationship between level and metalevel.
  • Relate spectral sequences, exact sequences and divisions of everything.
  • Understand what homotopy type theory has to say about the homotopy groups of spheres and thus Bott periodicity.
  • What is the relationship between loops - identity paths in Homotopy Type Theory - and strings in string theory?

Readings

Videos

Community

Rimvydas Krasauskas's interests

  • New foundations for mathematics
  • Having a real programming language to check proofs

Concepts:

  • Different levels of equivalences
  • Paths between points (homotopies) and equivalence of homotopies
  • Homotopy Type Theory Lecture Notes
  • In shulman see discussion of space and adjoint string and local topos.
  • In shulman how are dependent sum and dependent product adjoints?
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Šis puslapis paskutinį kartą keistas November 05, 2021, at 01:27 PM