단체 집합

노트

위키데이터

• ID : Q1467124

말뭉치

1. In mathematics, a simplicial set is an object made up of "simplices" in a specific way.
2. Formally, a simplicial set may be defined as a contravariant functor from the simplex category to the category of sets.
3. 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.
4. → CGHaus called the geometric realization taking a simplicial set X to its corresponding realization in the category of compactly-generated Hausdorff topological spaces.
5. 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.
6. 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.
7. If C C is a small category, the nerve of C C is a simplicial set which we denote NC NC .
8. 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.
9. \mapsto X_n\) by regarding the set \(X_n\) of \(n\)-simplices as a discrete or constant simplicial set.
10. We show that whenis a finite connected simplicial set, thencoincides with, the disjoint union of the Bousfield–Kan completion ofwith an external point.
11. The Barratt nerve - denoted B - is the endofunctor that takes a simplicial set to the nerve of the poset of its non-degenerate simplices.
12. This is a refinement to the result that any simplicial set can be triangulated.
13. A simplicial set is said to be regular if each of its non-degenerate simplices is embedded along its n-th face.
14. 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.
15. In a simplicial set, a simplex either is non-degenerate or is obtained by applying degeneracy maps to a non-degenerate simplex.
16. ¶ Return the ‘subdivision’ of simplex in this simplicial set into a pair of simplices.
17. An example involving an infinite simplicial set: sage: C3 = groups .

메타데이터

위키데이터

• ID : Q1467124

Spacy 패턴 목록

• [{'LOWER': 'simplicial'}, {'LEMMA': 'set'}]
• [{'LOWER': 'c.s.s'}, {'OP': '*'}, {'LEMMA': 'complex'}]
• [{'LOWER': 'simplical'}, {'LEMMA': 'set'}]