Homotopy Type Theory Permits 'Logic of Homotopy Types'
1. Idea. Proposed by Vladimir Voevodsky, Homotopy Type System (HTS) is a type theory with two equality types, an “exact” or “strict” one which ...
Homotopy type theory - (Algebraic Logic) - Fiveable
Homotopy type theory provides a new perspective on the foundations of mathematics, where types can represent both logical propositions and mathematical objects.
Propositional equality is interpreted as homotopy and type isomorphism as homotopy equivalence. Logical constructions in type theory then ...
Type Theory and Homotopy - andrew.cmu.ed
In doing so, it also permits logical methods to be combined with the traditional algebraic and topological approaches to homotopy theory, opening up a range of ...
Logic Across Disciplines- Homotopy Type Theory, the confluence of ...
University Seminar: Logic Across Disciplines- Homotopy Type Theory, the confluence of logic and space ... Abstract: In this talk we will learn how to express ...
Seminar on Homotopy Type Theory, Winter 2012 - Sandiego
On one hand, it enables us to apply homotopical ideas in type theory, giving new ways to deal with things like proof-irrelevance, singleton elimination, type ...
Homotopy Type Theory: What is it? - MathOverflow
It was noticed that you could intepret these types topologically: An object is a point, a proof of equality is a path, a proof that two proofs ...
Homotopy type theory - PlanetMath.org
Homotopy type theory ... A×B A × B ) as homotopy-invariant constructions on these spaces. In this way, we are able to manipulate spaces directly without first ...
Homotopy Type Theory, III | The n-Category Café
And of course, when restricted to sets, the above notion of equivalence for types can be regarded as the familiar notion of isomorphism (= ...
Constructive Type Theory and Homotopy - Steve Awodey - YouTube
... homotopy theory, especially in the modern treatment in terms of Quillen model categories and higher-dimensional categories. This talk will ...
Workshop on Homotopy Type Theory / Univalent Foundations
Homotopy Type Theory is a young area of logic, combining ideas from several established fields: the use of dependent type theory as a foundation for ...
Expressing 'the structure of' in homotopy type theory | Synthese
Abstract. As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type ...
Homotopy Type Theory: Concepts & Applications | Vaia
Homotopy Type Theory (HoTT) expands on traditional set theory by introducing types as mathematical objects, interpreted as spaces rather than sets. This ...
Homotopy Type Theory: The Logic of Space
Plotkin, Smyth, Abramsky, Vickers, Weihrauch and no doubt many others.” Page 3. 324. Michael Shulman particular topologies on computational data types but ...
Homotopy Type Theory: Univalent Foundations of Mathematics
Both logical propositions and sets are represented as types. Both proofs of propositions and elements of sets become elements of types.
Homotopy Type Theory - Google Groups
Sep 30. Workshop Categorical Logic and Higher Categories: registration. *** Workshop Categorical Logic and Higher Categories *** University of Manchester (UK), ...
Homotopy Type Theory is Martin Löf's dependent type theory together with Voevodsky's univalent axiom. This is a logic which aims at dealing with non-trivial ...
Homotopy Theory in Homotopy Type Theory: Introduction
Higher inductive types. To do some homotopy theory, we need some basic spaces (the circle, the sphere, the torus) and constructions for making ...
Practical example in using (homotopy) type theory - MathOverflow
G is a type · e:G, i:G→G, m:G×G→G · α is a proof of the identity stating associativity, and so on for λ,ρ,λ′,ρ′ which prove left and right ...
a basic introduction to homotopy type theory - UCSD
We'll start with types. 1. Types. Type theory1 is an alternative to the usual foundations of mathematics based on set theory and logic. Set theory ...