Towards a constructive simplicial model of Univalent Foundations

Univalent foundations as structuralist foundations

The Univalent Foundations of Mathematics (UF) provide not only an entirely non-Cantorian conception of the basic objects of mathematics (“homotopy types” instead of “sets”) but also a novel account of how foundations ought to relate to mathematical practice. In this paper, I intend to answer the question: In what way is UF a new foundation of mathematics? I will begin by connecting UF to a prag...

Univalent Foundations of Mathematics

Univalent Foundations Project

While working on the completion of the proof of the Bloch-Kato conjecture I have thought a lot about what to do next. Eventually I became convinced that the most interesting and important directions in current mathematics are the ones related to the transition into a new era which will be characterized by the widespread use of automated tools for proof construction and verification. I have star...

a tripartite model of efl teachers attributions, burnout, and ‎self-regulation: towards the prospects of effective teaching

همطالعه حاضر به ارائه مدلی برای آموزش موثر زبان انگلیسی ‏می پردازد. مدل حاضر از سه عامل تاثیر گذار در کارایی ‏تدریس معلمان زبان انگلیسی بهره می برد. این سه عامل شامل ‏سبکهای اسنادی، خود تنطیمی و فرسودگی شغلی معلمان ایرانی ‏زبان انگلیسی می باشد. رساله مورد نظر درچهار فاز طراحی ‏شده است: فاز اول شامل طراحی و رواسازی پرسشنامه سبکهای ‏اسنادی معلمان زبان انگلیسی و فاز دوم شامل استفاده از ‏این پرسشنا...

Univalent Semantics of Constructive Type Theories

In this talk I will outline a new semantics for dependent polymorphic type theories with Martin-Lof identity types. It is based on a class of models which interpret types as simplicial sets or topological spaces defined up to homotopy equivalence. The intuition based on the univalent semantics leads to new answers to some long standing questions of type theory providing in particular well-behav...