Simplicial objects in algebraic topology

By Jon P. May. 1993

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In Pure Mathematics

Citations in the corpus

On the Geometry of 2-Categories and their Classifying Spaces (2003, methodology): “For the general background on 2-categories used in this paper we refer to [1, 13], and on simplicial sets to [14].”
Anyons in an exactly solved model and beyond (2005, background): “d by homotopy theory because the fundamental homology class of the source (physical) manifold is involved. 29As explained to me by Ezra Getzler, higher groupoids may be nicely deﬁned as Kan complexes [99]; this approach also allows one to endow the morphism sets with topology. In the deﬁnition of Γ ”
The realization space of a Π-algebra: a moduli problem in algebraic topology (2004, unknown): “The main theorem 39 References 45”
More Concise Algebraic Topology: Localization, Completion, and Model Categories (2012, methodology): “We refer to the 1967 book [88], as reprinted in this series, for much of the background and details of definitions, although we could instead refer to the 1999”
Integrating $L_\infty $-algebras (2006, background): “Recall [May92, § I.4] that given a reduced Kan simplicial set X, its homotopy groups are given by πn(X) := {x ∈ Xn | di(x) = ∗ for all i}/ ∼, (15) where x ∼ x′ if there exists an element y ∈ Xn+1 such that d0(y) = x, d1(y) = x′, and di(y) = ∗ for all i > 1.”
NOTES ON 2-GROUPOIDS, 2-GROUPS AND CROSSED MODULES (2005, background): “That is, every two n-simplices that have equal boundaries and are homotopic relative to their common boundary are actually equal (see[Ma], §9 , or [GoJa], §I.”
The Local Structure of Algebraic K-Theory (2012, methodology): “For a general background on simplicial techniques the reader may consult the books of May [201], Gabriel and Zisman [89], Bousfield and Kan [40] or Goerss and Jardine [99].”
Partition Complexes, Tits Buildings and Symmetric Products (2001, background): “As a technical convenience, we take the term space on its own to mean simplicial set [ 15 ] [6].”