cubical geometric realisation in nLab
cubical geometric realisation in nLab
The category of cubical sets, just as with any reasonable category of shapes for higher structures, admits a geometric realisation functor to ...
Geometric realization is the special case of the general notion of nerve and realization that is induced from the standard cosimplicial topological space.
cubical set - exposition in nLab
the geometric realization of cartesian products of cubical sets (see geometric realization below) tends to have the wrong homotopy type: for ...
Notation 1.1. We make use of the notation of category of cubes. Definition 1.2. The category of cubical sets is the ...
Cubical stuff - Wiki - Evan Patterson
Literature · Sec. 1: Helpful summary of equivalent definitions of cube category · Sec. 2: Cubical sets and their geometric realization.
cubical-type model category in nLab
Whether they are equivalent by another map is not yet excluded. The question whether the geometric realization for the cubical sets based on ...
nForum - cubical geometric realisation - nLab
nLab > Latest Changes: cubical geometric realisation ... A little page dedicated to this construction, linked to from cubical set, and soon to be linked to from ...
model structure on cubical sets in nLab
2. Definition · weak equivalences are the morphisms that become weak equivalences under geometric realization | − | |-| ; · cofibrations are the ...
1. Idea · 2. The category of cubes · 3. Standard geometric cube functor · 4. Definition · 5. Relation between triangulation and cubulation · 6.
Categorification and the Cosmic Cube | The n-Category Café
... (nLab: univalence axiom), could one not use the opportunity of the nice geometric model of Ayala, Francis, and Rozenblyum to support intuitions?
What's special about the Simplex category? - MathOverflow
My understanding is that the realisation of cubical sets with connection only preserves finite products up to weak homotopy equivalence. Are you ...
The category of cubes has a concise description in category-theoretic terms but I would rather describe it like this: It's the category in which ...
The Functor of Points Approach to Schemes in Cubical Agda - arXiv
Keywords and phrases Schemes, Algebraic Geometry, Category Theory, Cubical Agda, Homotopy. Type Theory and Univalent Foundations ...
Conjectures in Grothendieck's "Pursuing stacks" - MathOverflow
The cubical setup is also not sufficient to describe the geometry underlying n-fold categories, and indeed there seems currently no name for ...
nLab -- General Discussion | The n-Category Café - Welcome
is regarded as a degenerate cube by the cubical set in all the possible ways. ... If you model a steel beam with a cell complex of geometric cells ...
introduction to quasicategories - Charles Rezk
... geometric realization, constructed explicitly geometric realization by. (20.7) ... of vertices in the cube, and that the only edges in ∆1 ⋄ ∆1 which ...
Triangulations of products of triangulations - Tim Hosgood
If we take the (geometric realisation of the) 1-cube (the interval ... See (as always) the nLab page on test categories.↩. I mean ...
connection on a cubical set in nLab
In the literature, two different definitions of connections on a cubical set are considered. The first definition treats edges of cubes as ...
... geometric morphism (LConst⊣Γ):H→Γ←LConst∞Grpd. In Top this is the usual ... nLab. Everything you find here is work in progress: please, edit it ...
Every simplicial set gives rise to a "nice" topological space, known as its geometric realization. This realization consists of geometric simplices, glued ...