Weak omega-categories from intensional type theory
نویسندگان
چکیده
منابع مشابه
Weak Ω-categories from Intensional Type Theory
We show that for any type in Martin-Löf Intensional Type Theory, the terms of that type and its higher identity types form a weak ω-category in the sense of Leinster. Precisely, we construct a contractible globular operad PMLId of definable “composition laws”, and give an action of this operad on the terms of any type and its identity types.
متن کاملWeak omega-categories
This paper proposes to define a weak higher-dimensional category to be a simplicial set satisfying properties. The definition is a refinement of that suggested at the end of [St3] which required extra structure on the simplicial set. The paper [St3] constructed the simplicial nerve of a (strict) ω-category. The principal aim of the paper was to prove that the construction was right adjoint to t...
متن کاملA Type-Theoretical Definition of Weak {\omega}-Categories
We introduce a dependent type theory whose models are weak ω-categories, generalizing Brunerie’s definition of ω-groupoids. Our type theory is based on the definition of ω-categories given by Maltsiniotis, himself inspired by Grothendieck’s approach to the definition of ω-groupoids. In this setup, ω-categories are defined as presheaves preserving globular colimits over a certain category, calle...
متن کاملInternalizing Intensional Type Theory
Homotopical interpretations of Martin-Löf type theory lead toward an interpretation of equality as a richer, more extensional notion. Extensional or axiomatic presentations of the theory with principles based on such models do not yet fully benefit from the power of dependent type theory, that is its computational character. Reconciling intensional type theory with this richer notion of equalit...
متن کاملIdempotents in intensional type theory
We study idempotents in intensional Martin-Löf type theory, and in particular the question of when and whether they split. We show that in the presence of propositional truncation and Voevodsky’s univalence axiom, there exist idempotents that do not split; thus in plain MLTT not all idempotents can be proven to split. On the other hand, assuming only function extensionality, an idempotent can b...
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: Logical Methods in Computer Science
سال: 2010
ISSN: 1860-5974
DOI: 10.2168/lmcs-6(3:24)2010