Homotopy type theory

Known as: Homotopic type theory, Fibrations-as-Types interpretation, Fibrations-as-types 
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intensional type theory, based on… (More)
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2018
2018
The notion of a natural model of type theory is defined in terms of that of a representable natural transfomation of presheaves… (More)
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2018
2018
We present a development of the theory of higher groups, including infinity groups and connective spectra, in homotopy type… (More)
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2017
2017
We discuss the homotopy type theory library in the Lean proof assistant. The library is especially geared toward synthetic… (More)
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2017
2017
Univalent homotopy type theory (HoTT) may be seen as a language for the category of ∞-groupoids. It is being developed as a new… (More)
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2016
2016
Broadly speaking, algebraic topology consists of associating algebraic structures to topological spaces that give information… (More)
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2015
2015
Homotopy Type Theory may be seen as an internal language for the ∞category of weak ∞-groupoids which in particular models the… (More)
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2015
2015
We will give a detailed account of why the simplicial sets model of the univalence axiom due to Voevodsky also models W-types. In… (More)
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2014
2014
Martin-Löf’s Extensional Type Theory (ETT) has a straighforward semantics in the category Set of sets and functions and actually… (More)
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2014
2014
We give a glimpse of an emerging field at the intersection of homotopy theory, logic, and theoretical computer science: homotopy… (More)
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2012
2012
Homotopy type theory is an interpretation of Martin-Löf's constructive type theory into abstract homotopy theory. There results… (More)
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