Simplicial matrices and the nerves of weak -categories I: Nerves of bicategories.
Duskin, John W. (2001)
Theory and Applications of Categories [electronic only]
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Displaying similar documents to “On the nerve of an -category”
Simplicial matrices and the nerves of weak -categories I: Nerves of bicategories.
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In this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of εn. First we introduce the Lebesgue number, which for an arbitrary open cover of a compact metric space M is a positive real number so that any ball of about such radius must be completely contained in a member of the cover. Then we introduce the notion of a bounded simplicial complex and the diameter of a bounded simplicial complex....
Moment-angle complexes from simplicial posets
Zhi Lü, Taras Panov (2011)
Open Mathematics
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We extend the construction of moment-angle complexes to simplicial posets by associating a certain T m-space Z S to an arbitrary simplicial poset S on m vertices. Face rings ℤ[S] of simplicial posets generalise those of simplicial complexes, and give rise to new classes of Gorenstein and Cohen-Macaulay rings. Our primary motivation is to study the face rings ℤ[S] by topological methods. The space Z S has many important topological properties of the original moment-angle complex Z K associated...
Simplicial approximation.
Jardine, J.F. (2004)
Theory and Applications of Categories [electronic only]
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