- geometric realization in nLab🔍
- geometric realization of categories in nLab🔍
- geometric realization of simplicial topological spaces in nLab🔍
- nerve and realization in nLab🔍
- Simplicial set🔍
- cubical geometric realisation in nLab🔍
- Homotopy equivalence of geometric realizations🔍
- simplicial complex in nLab🔍
geometric realization in nLab
That geometric realization preserves products is sensitive to whether we think of it as valued in Top Top or in a convenient category Space ...
geometric realization of categories in nLab
Geometric realization of categories is a functor that sends categories to topological spaces, namely the functor which first forms the simplicial set.
geometric realization of simplicial topological spaces in nLab
A simplicial topological space, its geometric realization is the coend | X • | ≔ ∫ n ∈ Δ X n × Δ Top n {|X_\bullet|} \coloneqq \int^{n \
Topological realization of simplicial sets · The corresponding realization is what is traditionally called geometric realization of simplicial ...
Every simplicial set gives rise to a "nice" topological space, known as its geometric realization. This realization consists of geometric simplices, glued ...
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 ...
Homotopy equivalence of geometric realizations - MathOverflow
Yes. If you are given a simplicial set X:Δop→Sets, then the the thick realization ||X|| of X is given by the same formula as the ordinary ...
A space is triangulable if and only if it is homeomorphic to the geometric realization of a simplicial set. As an important step: The geometric ...
Help me gain some intuition for the simplex category
nLab gives a bunch of other, fairly high level definitions that I ... Sing turns out to have a left adjoint given by geometric realization ...
geometric realization of cohesive infinity-groupoids in nLab
1. Definition ... the geometric realization functor. For X ∈ H X \in \mathbf{H} any object, hence any cohesive ∞-groupoid, | Π ( X ) | \vert \Pi(X)\ ...
Nerve (category theory) - Wikipedia
The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely related objects can ...
geometric realization of simplicial topological spaces - nForum
It says that geometric realization is preserved by homotopy pullback along every morphism, but what I'd need is only that it's preserved for one particular ...
Does geometric realization commute with finite limits?
It is for instance shown here on the nLab. Note that we must assume Top is a convenient category of topological spaces, not the category of ...
Why study simplicial homotopy groups? - MathOverflow
... geometric realization.(cf. http://ncatlab.org/nlab/show/model+structure+on+simplicial+sets). As I understand it so far, the only satisfactory ...
It is these two functors that provide the Quillen equivalence between simplicial sets and spaces. The geometric realization functor is important ...
Publications of the nLab | The n-Category Café
We have made this happen for instance with the entry geometric realization of simplicial topological spaces, after we noticed that it was being ...
Cubical stuff - Wiki - Evan Patterson
2: Cubical sets and their geometric realization. Homotopy. Brown & Higgins ... Brown, Higgins, Sivera, 2011: Nonabelian algebraic topology (doi, pdf, nLab ), Ch.
Homotopy realizations are a special case of homotopy colimits, when the indexing diagram is Δ op \Delta^{op}, the opposite category of the category of ...
sarahzrf on X: "ive seen two ways of writing down explicit standard n ...
... geometric realization functors |-| : Δ → Top. (nlab calls them ... (nlab calls them "barycentric" and "cartesian") is either one More ...
Simplicial Sets vs. Simplicial Complexes | The n-Category Café
Per nLab, [ X ] [X] is the space of probability measures on the ... with the property that the geometric realization of the abstract ...