Cubical Covers of Sets in R^n
نویسندگان
چکیده
منابع مشابه
Varieties of Cubical Sets
We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories. We prove that all our sites are test categories in the sense of Grothendieck, meaning that the corresponding presheaf categories of cubical sets model classical homotopy theory. We delineate exactly which ones are even strict test categories, me...
متن کاملVariation on Cubical sets
In the model presented in [1, 4] a type is interpreted by a nominal set A equipped with two “face” operations: if u : A and i is a symbol we can form u(i = 0) : A(i = 0) and u(i = 1) : A(i = 1) elements independent of i. The unit interval is represented by the nominal set I, whose elements are 0, 1 and the symbols. Alternatively, we have a presentation as a presheaf category over the category w...
متن کاملA category of cubical sets
The base category C is the full subcategory of the category of posets having for objects finite power of the poset 0 6 1. We write [1] the poset 0 6 1. We write I, J,K, . . . the object of C and 1I : I → I the identity map of I. If f : J → I and g : K → J we write fg : K → I their composition. If I is an object of C, we have two constant maps c0 : I → [1] and c1 : I → [1]. We write π1 : I × [1]...
متن کاملLecture Notes on Cubical sets
These are some lecture notes for a course presenting the cubical set model of type theory, first in Copenhagen, December 2014, and then in Paris, February 2015. We describe a particular presheaf model of type theory. This description can also be seen as an operational semantics of a purely syntactical type system. It involves a nominal extension of λ-calculus. We use a generalization of the Kan...
متن کاملLecture Notes on Cubical sets
These are some lecture notes for a course presenting the cubical set model of type theory, first in Copenhagen, December 2014, and then in Paris, February 2015. We describe a particular presheaf model of type theory. This description can also be seen as an operational semantics of a purely syntactical type system. It involves a nominal extension of λ-calculus. We use a generalization of the Kan...
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: New Trends in Mathematical Science
سال: 2019
ISSN: 2147-5520
DOI: 10.20852/ntmsci.2019.392