en>John of Reading: Typo/general fixing, replaced: build-in → built-in; removed leftover AFC comment using AWB

2014-09-02T16:13:03Z

Typo/general fixing, replaced: build-in → built-in; removed leftover AFC comment using AWB

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	~~In topology~~, a ~~branch of mathematics~~, ~~given~~ a ~~topological monoid~~ '~~'X'' up~~ to ~~homotopy (~~in a ~~nice way)~~, an ~~'''infinite loop space machine''' produces~~ a ~~[[group completion]]~~ of ~~''X'' together~~ with ~~[[infinite loop space]] structure~~. For ~~example~~, ~~one can take ''X''~~ to be the ~~[[classifying space]]~~ of a ~~[[symmetric monoidal category]] ''S'';~~ that is, <~~math~~>~~X = BS~~<~~/math~~>. ~~Then~~ the ~~machine produces~~ the ~~group completion~~ <~~math~~>~~BS \to K(S)~~<~~/math~~>~~. The space~~ <~~math~~>~~K(S)~~</~~math>~~ may ~~be described by~~ the ~~[[K-theory spectrum]] of ''S~~''.

	~~== References ==~~
	*May, [http://~~www~~.~~math~~.~~uchicago~~.~~edu~~/~~~may/PAPERS/22~~.~~pdf The uniqueness~~ of ~~infinite loop space machine]~~

	~~[[Category:Homotopy theory]]~~
	~~[[Category:Topological spaces]]~~
	~~[[Category:Topology]]~~

	~~{{topology-stub}}~~

en>Pandadai: /* Estimation */

2013-12-05T01:13:03Z

Estimation

New page

{{orphan|date=December 2013}}
In topology, a branch of mathematics, given a topological monoid ''X'' up to homotopy (in a nice way), an '''infinite loop space machine''' produces a [[group completion]] of ''X'' together with [[infinite loop space]] structure. For example, one can take ''X'' to be the [[classifying space]] of a [[symmetric monoidal category]] ''S''; that is, <math>X = BS</math>. Then the machine produces the group completion <math>BS \to K(S)</math>. The space <math>K(S)</math> may be described by the [[K-theory spectrum]] of ''S''.

== References ==
*May, [http://www.math.uchicago.edu/~may/PAPERS/22.pdf The uniqueness of infinite loop space machine]

[[Category:Homotopy theory]]
[[Category:Topological spaces]]
[[Category:Topology]]

{{topology-stub}}

Functional principal component analysis - Revision history

en>John of Reading: Typo/general fixing, replaced: build-in → built-in; removed leftover AFC comment using AWB

en>Pandadai: /* Estimation */