topology, a theorem of Milnor says that the geometric realization functor from the homotopy category of the category Kan of Kan complexes to the homotopy...

(the Brown representability theorem). See also: Milnor's theorem on Kan complexes Abstract cell complex The notion of CW complex has an adaptation to smooth...

Y)\cong {\text{Hom}}_{s{\text{Sets}}}(X,S(Y))} See also: Milnor's theorem on Kan complexes. It can be shown that the simplicial set underlying a simplicial...

group laws Crossed module Milnor's theorem on Kan complexes Fibration of simplicial sets May, Ch. 8. § 3. May, Ch 4. § 5. Milnor 1959, Corollary 1. NB: "second...

simplicial sets, Kan complexes and CW complexes being given by the geometric realization and the singular functor (Milnor's theorem). The Kan–Quillen model...

to define ∞-groupoids simply as Kan complexes. Now, a theorem of Milnor and CW approximation says that Kan complexes completely determine the homotopy theory...

Kampen's theorem." Brown, Ronald; Higgins, Philip J.; Sivera, Rafael (2011), Nonabelian Algebraic Topology: Filtered Spaces, Crossed Complexes, Cubical...

from texts on other topics or journal articles. John Milnor This short book introduces the main concepts of differential topology in Milnor's lucid and...

between CW complexes is cellular if f ( X n ) ⊂ Y n {\displaystyle f(X^{n})\subset Y^{n}} for all n. 2.  The cellular approximation theorem says that every...

example in the ungraded situation is a chain complex C•. An object C• in an abelian category of chain complexes naturally comes with a differential d. Let...