About constructive mathematics and Homotopy type theory

So if you insist on doing things classically in Homotopy Type Theory, you may do so to your hearts content. You will only loose a bit of ...

Constructivity in Homotopy Type Theory

In the seminal HoTT Book (2013), it is maintained that constructive reasoning is not necessary when formalizing mathematics in homotopy type theory. (HoTT):.

Homotopy Type Theory: What is it? - MathOverflow

Topologists are seeing type theory as a concise and convenient ways to reason about topology, where equalities are interpreted as paths (and ...

Constructive Type Theory and Homotopy - Steve Awodey - YouTube

... constructive mathematics, especially as formulated in the type theory of Martin-Löf, and homotopy theory, especially in the modern treatment ...

Does Homotopy Type Theory Provide a Foundation for Mathematics?

in constructive intensional type theory that offers an alternative to the foundations provided by ZFC set theory and category theory. This ...

Homotopy Type Theory, I | The n-Category Café - Welcome

In subsequent posts, I'll say a bit about what mathematics looks like when done in homotopy type theory, and about some homotopically motivated ...

nLab mathematics presented in homotopy type theory

Homotopy type theory is a formal language in which it is possible to carry out synthetic mathematics using proof assistants, such as Coq and Agda. This is also ...

Homotopy Type Theory: Univalent Foundations of Mathematics

... constructive mathematics. In what follows, we will often use “type theory” to refer specifically to this system and similar ones, although type theory as a ...

Eric Finster : Homotopy Theory and Constructive Mathematics

Constructive mathematicians and computer scientists have long been interested in logical theories in which all mathematical statements have ...

[2212.11082] Introduction to Homotopy Type Theory : r/math - Reddit

Homotopy type theory is exactly a form of constructive higher order logic with the univalence axiom. As well as being a useful setting for ...

Type Theory and Homotopy - andrew.cmu.ed

Indeed, Martin-Löf type theory has been used successfully to formalize large parts of constructive mathematics, such as the theory of general- ized ...

Homotopy Type Theory: Unified Foundations of Mathematics and ...

and structure, in both constructive mathematics and homotopy theory. The univalent approach of homotopy type theory exploits the axiomatic ...

What is Homotopy Type Theory, and what implications does it hold?

Homotopy theory is an advanced branch of topology which studies a weak notion of equivalence between spaces called homotopy equivalence. All ...

homotopy type theory FAQ in nLab

Homotopy type theory is a refinement of constructive set theory that takes fully seriously the constructive nature also of identity. (As with ...

Does Homotopy Type Theory Provide a Foundation for Mathematics?

Homotopy Type Theory (HoTT) is a putative new foundation for mathematics grounded in constructive intensional type theory that offers an alternative to the ...

A Primer on Homotopy Type Theory Part 1 - PhilSci-Archive

The use of constructive logic also enables us to give a firmer philosophical basis for the resulting foundation for mathematics, and eliminates ...

Homotopy Type Theory - Steve Awodey

▷ Martin-Löf type theory (a formal system of constructive foundations) can be interpreted into abstract homotopy theory. (the mathematics of continuous space).

Homotopy Type Theory

Homotopy Type Theory refers to a new field of study relating Martin-Löf's system of intensional, constructive type theory with abstract homotopy ...

Homotopy type theory - Wikipedia

In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the ...

Intuitionistic Type Theory - Stanford Encyclopedia of Philosophy

Intuitionistic type theory (also constructive type theory or Martin-Löf type theory) is a formal logical system and philosophical foundation ...