Spaces of directed paths on pre-cubical sets II
نویسندگان
چکیده
منابع مشابه
Variation 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 کاملLimits and colimits in the category of pre-directed complete pre-ordered sets
In this paper, some categorical properties of the category { Pre-Dcpo} of all pre-dcpos; pre-ordered sets which are also pre-directed complete, with pre-continuous maps between them is considered. In particular, we characterize products and coproducts in this category. Furthermore, we show that this category is neither complete nor cocomplete. Also, epimorphisms and monomorphisms in {Pre-Dcpo} ...
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 کاملVarieties 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 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: Journal of Applied and Computational Topology
سال: 2019
ISSN: 2367-1726,2367-1734
DOI: 10.1007/s41468-019-00040-z