Simplicial Homotopy Theory

By Paul G. Goerss, John F. Jardine. 2009

1,465 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Management Science and Operations Research, Mathematical Physics, Pure Mathematics

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Citations in the corpus

UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2018, background): “These functors are the natural extension of the classical realization and singular set functors from algebraic topology (see [7] or [16] for example).”
The simplicial model of Univalent Foundations (after Voevodsky) (2012, positive): “For the homotopy-theoretic aspects, [GJ09] and [Hov99] are both excellent and suﬃcient references.”
Props in model categories and homotopy invariance of structures (2008, background): “2125] and further references therein); – the category of simplicial sets S (see for instance [16] and [24, §3]); – the category of (possibly unbounded) dg-modules dg kMod, where k denotes any fixed ground ring (see for instance [24, §2.”
Symmetric monoidal structure on non-commutative motives (2010, background): “The reader unfamiliar with this language is invited to consult Goerss & Jardine [20], Hirschhorn [23], Hovey [24], or Quillen’s ha l-0 04 61 94 1, v er si on 1 7 M ar 2 01 0”
Cotorsion pairs and model categories (2007, background): “It is not at allobvious that this is a cotorsion pair,or what cotorsion m odules look like.”
A universal characterization of higher algebraic K-theory (2010, background): “ objects. In model categories, there is a well-developed theory of Bousﬁeld localization (e.g., Hirschhorn’s comprehensive discussion in [42], Goerss and Jardine’s treatment in the simplicial setting [37], or the exposition of Smith’s theory for combinatorial model categories in [2]). Because locali”
Reparametrizations of continuous paths (2007, background): “estigation of invariantsofd-spacesin [15]. Further possibleareasofapplicationofthe results (and of higher-dimensionsal generalisations still to be investigated) include categorical homotopytheoryasin [8], categoriﬁedgaugetheoryasin [1] andn-transporttheory; cf. the blog “The n-category caf´e” at htt”