Ambrus Kaposi, Quotient inductive-inductive types and higher friends скачать в хорошем качестве

Ambrus Kaposi, Quotient inductive-inductive types and higher friends

Homotopy Type Theory Electronic Seminar Talks, 2020-10-22 https://www.uwo.ca/math/faculty/kapul... Quotient inductive-inductive types (QIITs) are generalisations of inductive types where we allow multiple sorts indexed over each other and we allow equality constructors. QIITs can also be seen as initial algebras for generalised algebraic theories. In this talk I will show a simple direct definition of QIITs, explain their categorical semantics and give a survey of the current results about existence of initial algebras. I will also describe two extensions: higher inductive-inductive types and higher order abstract syntax. Joint work with Thorsten Altenkirch, Rafaël Bocquet, Paolo Capriotti, András Kovács, Ambroise Lafont, Christian Sattler, and Zongpu (Szumi) Xie.