Univalence for inverse diagrams and homotopy canonicity
نویسندگان
چکیده
منابع مشابه
Univalence for inverse diagrams and homotopy canonicity
We describe a homotopical version of the relational and gluing models of type theory, and generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy theory on inverse diagrams, and relies on the fact that Reedy fibrant diagrams correspond to contexts of a certain shape in type theory. This has two main applications. First, by considering inverse diagrams in Voevodsky...
متن کاملVoevodsky’s Univalence Axiom in homotopy type theory
In this short note we give a glimpse of homotopy type theory, a new field of mathematics at the intersection of algebraic topology and mathematical logic, and we explain Vladimir Voevodsky’s univalent interpretation of it. This interpretation has given rise to the univalent foundations program, which is the topic of the current special year at the Institute for Advanced Study. The Institute for...
متن کاملHomotopy theory of diagrams
In this paper we develop homotopy theoretical methods for studying diagrams. In particular we explain how to construct homotopy colimits and limits in an arbitrary model category. The key concept we introduce is that of a model approximation. A model approximation of a category C with a given class of weak equivalences is a model category M together with a pair of adjoint functors M ⇄ C which s...
متن کاملHomotopy Theories of Diagrams
Suppose that S is a space. There is an injective and a projective model structure for the resulting category of spaces with S-action, and both are easily derived. These model structures are special cases of model structures for presheaf-valued diagrams X defined on a fixed presheaf of categories E which is enriched in simplicial sets. Varying the parameter category object E (or parameter space ...
متن کاملSemiring Labelled Decision Diagrams, Revisited: Canonicity and Spatial Efficiency Issues
Existing languages in the valued decision diagrams (VDDs) family, including ADD, AADD, and those of the SLDD family, prove to be valuable target languages for compiling multivariate functions. However, their efficiency is directly related to the size of the compiled formulae. In practice, the existence of canonical forms may have a major impact on the size of the compiled VDDs. While efficient ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 2014
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129514000565