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위키데이터
- ID : Q1467124
말뭉치
- In mathematics, a simplicial set is an object made up of "simplices" in a specific way.[1]
- Formally, a simplicial set may be defined as a contravariant functor from the simplex category to the category of sets.[1]
- One may view a simplicial set as a purely combinatorial construction designed to capture the notion of a "well-behaved" topological space for the purposes of homotopy theory.[1]
- → CGHaus called the geometric realization taking a simplicial set X to its corresponding realization in the category of compactly-generated Hausdorff topological spaces.[1]
- Simplicial sets generalize the idea of simplicial complexes: a simplicial set is like a combinatorial space built up out of gluing abstract simplices to each other.[2]
- They depend on lower dimensional features, (notice however that a simplicial set by itself is not equipped with any notion of composition of simplices, nor really, therefore, of identities.[2]
- If C C is a small category, the nerve of C C is a simplicial set which we denote NC NC .[2]
- The importance of full simplicial sets lies in the fact that the relation of homotopy between simplicial mappings from an arbitrary simplicial set to a full simplicial set is an equivalence relation.[3]
- \mapsto X_n\) by regarding the set \(X_n\) of \(n\)-simplices as a discrete or constant simplicial set.[4]
- We show that whenis a finite connected simplicial set, thencoincides with, the disjoint union of the Bousfield–Kan completion ofwith an external point.[5]
- The Barratt nerve - denoted B - is the endofunctor that takes a simplicial set to the nerve of the poset of its non-degenerate simplices.[6]
- This is a refinement to the result that any simplicial set can be triangulated.[6]
- A simplicial set is said to be regular if each of its non-degenerate simplices is embedded along its n-th face.[6]
- A simplicial set \(X\) is a collection of sets \(X_n\) indexed by the non-negative integers; the set \(X_n\) is called the set of \(n\)-simplices.[7]
- In a simplicial set, a simplex either is non-degenerate or is obtained by applying degeneracy maps to a non-degenerate simplex.[7]
- ¶ Return the ‘subdivision’ of simplex in this simplicial set into a pair of simplices.[7]
- An example involving an infinite simplicial set: sage: C3 = groups .[7]
소스
- ↑ 1.0 1.1 1.2 1.3 Simplicial set
- ↑ 2.0 2.1 2.2 simplicial set in nLab
- ↑ Encyclopedia of Mathematics
- ↑ Turning simplicial complexes into simplicial sets
- ↑ Homotopy theory of complete Lie algebras and Lie models of simplicial sets
- ↑ 6.0 6.1 6.2 Non-singular simplicial sets
- ↑ 7.0 7.1 7.2 7.3 Simplicial sets — Sage 9.2 Reference Manual: Cell complexes and their homology
메타데이터
위키데이터
- ID : Q1467124
Spacy 패턴 목록
- [{'LOWER': 'simplicial'}, {'LEMMA': 'set'}]
- [{'LOWER': 'c.s.s'}, {'OP': '*'}, {'LEMMA': 'complex'}]
- [{'LOWER': 'simplical'}, {'LEMMA': 'set'}]