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Sunday, November 10, 2019

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Simplicial Homotopy Theory Modern Birkhäuser Classics ~ Zentralblatt MATH … they succeed The book is an excellent account of simplicial homotopy theory from a modern point of view … The book is well written … The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques andor the theory of simplicial closed model categories Mathematical Reviews

Simplicial set Wikipedia ~ In mathematics a simplicial set is an object made up of simplices in a specific way Simplicial sets are higherdimensional generalizations of directed graphs partially ordered sets and categories

Simplicial Homotopy Theory SpringerLink ~ Part of the Progress in Mathematics book series PM volume 174 Log in to check access Simplicial functors and homotopy coherence Paul G Goerss John F Jardine Pages 431462 Algebraic Ktheory Algebraic topology Homological algebra Homotopy Ktheory algebra colimit homology homotopy theory Authors and affiliations Paul G

ADVANCES IN MATHEMATICS University of Rochester ~ SIMPLICIAL HOMOTOPY THEORY 111 subsimplicial set of K which contains all the nondegenerate simplices of K of dimension n Arguments sometimes go by induction on the nondegenerate simplices or by induction on the skeletons in analogy with CW spaces

Simplicial Homotopy Theory RAS ~ The origin of simplicial homotopy theory coincides with the beginning of alge braic topology almost a century ago The thread of ideas started with the work of Poincar´e and continued to the middle part of the 20th century in the form of combinatorial topology

Categorical homotopy theory Emily Riehl Mathematics ~ For instance it is well known that the homotopy category of a simplicial model category is enriched over the homotopy category of spaces Following Shu09 we present a general framework that detects when derived functors and more exotic structures such as weighted homotopy colimits admit compatible enrich ments

simplicial homotopy group in nLab ~ Paul Goerss Rick Jardine chapter I section 7 of Simplicial homotopy theory Progress in Mathematics Birkhäuser 1996 Originally homotopy groups of simplicial sets had been defined in terms of the ordinary homotopy groups of the topological spaces realizing them Apparently the first or one of the first discussions of the purely

Hurewicz theorem Wikipedia ~ In mathematics the Hurewicz theorem is a basic result of algebraic topology connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism The theorem is named after Witold Hurewicz and generalizes earlier results of Henri Poincaré

simplicial skeleton in nLab ~ models topological simplicial localic … see also algebraic topology Introductions Introduction to Basic Homotopy Theory Introduction to Abstract Homotopy Theory geometry of physics – homotopy types Definitions homotopy higher homotopy homotopy type Pialgebra spherical object and PiAalgebra homotopy coherent category


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