Homotopy Type Theory
In mathematical logic and computer science, homotopy type theory (HoTT ) refers to various lines of development of intuitionistic type theory, based on the interpretation of types as objects to which the intuition of (abstract) homotopy theory applies. This includes, among other lines of work, the construction of homotopical and higher-categorical models for such type theories; the use of type theory as a logic (or internal language) for abstract homotopy theory and higher category theory; the development of mathematics within a type-theoretic foundation (including both previously existing mathematics and new mathematics that homotopical types make possible); and the formalization of each of these in computer proof assistants. There is a large overlap between the work referred to as homotopy type theory, and as the univalent foundations project. Although neither is precisely delineated, and the terms are sometimes used interchangeably, the choice of usage also sometimes ...
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Hott Book Cover
HOTT may refer to: *Mathematics: **Homotopy type theory *Games: **'' Halls of the Things'', an early video game ** ''Hordes of the Things'' (wargame) *Entertainment: **"Hanging on the Telephone", a song by the power pop band The Nerves, also recorded by Blondie ** Hour of the Time, a shortwave radio show *Other: **Hot Topic Hot Topic, Inc. (stylized as HOT TOPIC) is an American retail chain specializing in counterculture-related clothing and accessories, as well as licensed music. The stores are aimed towards an audience interested in rock music and video gaming ...

Homotopical Algebra
In mathematics, homotopical algebra is a collection of concepts comprising the ''nonabelian'' aspects of homological algebra as well as possibly the abelian aspects as special cases. The ''homotopical'' nomenclature stems from the fact that a common approach to such generalizations is via abstract homotopy theory, as in nonabelian algebraic topology, and in particular the theory of closed model categories. This subject has received much attention in recent years due to new foundational work of Vladimir Voevodsky, Eric Friedlander, Andrei Suslin, and others resulting in the A1 homotopy theory for quasiprojective varieties over a field. Voevodsky has used this new algebraic homotopy theory to prove the Milnor conjecture (for which he was awarded the Fields Medal) and later, in collaboration with Markus Rost, the full Bloch–Kato conjecture. References * * * See also *Derived algebraic geometry * Derivator * Cotangent complex - one of the first objects discovered u ...
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