simplicial set

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• Simplicial set — In mathematics, a simplicial set is a construction in categorical homotopy theory which is a purely algebraic model of the notion of a well behaved topological space. Historically, this model arose from earlier work in combinatorial topology and… …   Wikipedia

• Pro-simplicial set — In mathematics, a pro simplicial set is an inverse system of simplicial sets.A pro simplicial set is called pro finite if each term of the inverse system of simplicial sets has finite homotopy groups.Pro simplicial sets show up in shape theory,… …   Wikipedia

• Simplicial complex — In mathematics, a simplicial complex is a topological space of a particular kind, constructed by gluing together points, line segments, triangles, and their n dimensional counterparts (see illustration). Simplicial complexes should not be… …   Wikipedia

• Simplicial category — In mathematics, the simplicial category (or ordinal category) is a construction in category theory used to define simplicial and cosimplicial objects. Formal definitionThe simplicial category is usually denoted by Delta and is sometimes denoted… …   Wikipedia

• Simplicial homology — In mathematics, in the area of algebraic topology, simplicial homology is a theory with a finitary definition, and is probably the most tangible variant of homology theory. Simplicial homology concerns topological spaces whose building blocks are …   Wikipedia

• Simplicial manifold — In mathematics, the term simplicial manifold commonly refers to either of two different types of objects, which combine attributes of a simplex with those of a manifold. Briefly; a simplex is a generalization of the concept of a triangle into… …   Wikipedia

• Delta set — In mathematics, a delta set (or Δ set) S is a combinatorial object that is useful in the construction and triangulation of topological spaces, and also in the computation of related algebraic invariants of such spaces. A delta set is somewhat… …   Wikipedia

• Abstract simplicial complex — In mathematics, an abstract simplicial complex is a purely combinatorial description of the geometric notion of a simplicial complex, consisting of a family of finite sets closed under the operation of taking subsets. In the context of matroids… …   Wikipedia

• Dendroidal set — In mathematics, a dendroidal set is a generalization of simplicial sets introduced by Moerdijk Weiss (2007). They have the same relation to (colored symmetric) operads, also called symmetric multicategories, that simplicial sets have to… …   Wikipedia

• Causal set theory bibliography — Main article: Causal Sets This Causal Set Theory Bibliography is intended to aid causal set research. It gathers together academic papers, books, talks and PhD theses related to causal set theory and is intended to help readers find references… …   Wikipedia

• Kan fibration — The notion of a Kan fibration is a part of the theory of simplicial sets in mathematics. Kan fibrations are the fibrations in the model category theoretic sense on the category of simplicial sets and are therefore of fundamental importance. The… …   Wikipedia