mathematics, a simplicial set is a sequence of sets with internal order structure (abstract simplices) and maps between them. Simplicial sets are higher-dimensional...

mathematics, the extension of simplicial sets (extension functor or Ex functor) is an endofunctor on the category of simplicial sets. Due to many remarkable...

of a right fibration of simplicial sets in the ∞-category setup. A left anodyne extension is a map in the saturation of the set of the horn inclusions...

A simplicial map (also called simplicial mapping) is a function between two simplicial complexes, with the property that the images of the vertices of...

Extension (semantics), the set of things to which a property applies Extension (simplicial set) Extension by definitions Extensional definition, a definition...

subdivision of simplicial sets plays an important role in the extension of simplicial sets right adjoint to it. For a partially ordered set I {\displaystyle...

part of the theory of simplicial sets. Kan fibrations are the fibrations of the standard model category structure on simplicial sets and are therefore of...

bisimplicial set is a simplicial object in the category of simplicial sets, which themselves are simplicial objects in the category of sets. Many concepts...

topological properties of simplicial complexes and their generalizations, cell-complexes. An abstract simplicial complex above a set V {\displaystyle V} is...

standard way to subdivide a given simplex into smaller ones. Its extension to simplicial complexes is a canonical method to refining them. Therefore, the...

characteristics, advantages, and limitations: Simplicial complexes Simplest form of higher-order domains. Extensions of graph-based models. Admit hierarchical...

any set in the family also belong to the family forms an abstract simplicial complex. An incidence structure consists of a set of points, a set of lines...

inserting or deleting elements of the orderings. (See simplicial set for relations of these maps.) A simplicial object is a presheaf on Δ {\displaystyle \Delta...

The set of Gödel numbers is computable. The set of Turing machines that halt is not computable. The set of pairs of homeomorphic finite simplicial complexes...

topology, since it is locally Euclidean. Similarly, every simplex and every simplicial complex inherits a natural topology from Rn. The Zariski topology is defined...

optimization method with inequality constraints Simplicial complex Simplicial homology Simplicial set Spectrahedron Ternary plot Elte, E.L. (2006) [1912]...

topologists. The third theorem is perhaps the hardest. Brouwer also proved the simplicial approximation theorem in the foundations of algebraic topology, which...

which make the task easier. The simplicial homology groups Hn(X) of a simplicial complex X are defined using the simplicial chain complex C(X), with Cn(X)...

model structure on the category of simplicial sets. It consists of three classes of morphisms between simplicial sets called fibrations, cofibrations and...

In mathematics, a simplicially enriched category, is a category enriched over the category of simplicial sets. Simplicially enriched categories are often...

model uses Kan complexes which are fibrant objects in the category of simplicial sets (with the standard model structure). It is an ∞-category generalization...

{V} } as a V {\displaystyle \mathbf {V} } -valued presheaf. A simplicial set is a Set-valued presheaf on the simplex category C = Δ {\displaystyle C=\Delta...

topos a pro-simplicial set (up to homotopy). (It's better to consider it in Ho(pro-SS); see Edwards) Using this inverse system of simplicial sets one may...

Review of the Causal Set Approach to Quantum Gravity and A Growth Dynamics for Causal Sets; Presented at "New Directions in Simplicial Quantum Gravity" July...

mid-1950s he made distinguished contributions to the theory of simplicial sets and simplicial methods in topology in general. In recognition of this, the...

Simplex Simplicial complex Polytope Triangulation Barycentric subdivision Simplicial approximation theorem Abstract simplicial complex Simplicial set Simplicial...

spaces often admit a model category structure, such as the category of simplicial sets. Another model category is the category of chain complexes of R-modules...

bifiltration is a simplicial filtration used in topological data analysis for analyzing the shape of point cloud data. It is a multiparameter extension of the Vietoris–Rips...

In mathematics, more precisely, in the theory of simplicial sets, the Dold–Kan correspondence (named after Albrecht Dold and Daniel Kan) states that there...

lemma Polytope Simplex Simplicial complex CW complex Manifold Triangulation Barycentric subdivision Sperner's lemma Simplicial approximation theorem Nerve...