Simple rational approximation - Revision history

en>Worldbruce: Unlinked from disambiguation page

2014-08-28T23:30:15Z

Unlinked from disambiguation page

← Older revision		Revision as of 01:30, 29 August 2014
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	~~{{Unreferenced\|date=March 2009}}~~		Ed is what people call me and my spouse doesn't like it at all. Since he was eighteen he's been operating as an info officer but he plans on changing it. For a while I've been in Alaska but I will have to transfer in a year or two. What me and my family members love is to climb but I'm considering on starting some thing new.<br><br>Check out my site; [http://mybrandcp.com/xe/board_XmDx25/107997 tarot readings]
	~~Suppose that <math>(\mathcal C,\otimes,I)</math>~~ and ~~<math>(\mathcal D,\bullet,J)</math> are two [[monoidal category\|monoidal categories]]~~. ~~A '''monoidal adjunction~~'~~'' between two [[lax monoidal functor]]~~s
	~~:<math>(F,m):(\mathcal C,\otimes,I)\to (\mathcal D,\bullet,J)</math> and <math>(G,n):(\mathcal D,\bullet,J)\to(\mathcal C,\otimes,I)</math>~~
	is an ~~[[Adjoint functors\|adjunction]] <math>(F,G,\eta,\varepsilon)</math> between the underlying functors, such that the [[natural transformation]]s~~
	~~:<math>\eta:1_{\mathcal C}\Rightarrow G\circ F</math> and <math>\varepsilon:F\circ G\Rightarrow 1_{\mathcal D}</math>~~
	~~are [[monoidal natural transformation]]s~~.

	~~== Lifting adjunctions to monoidal adjunctions ==~~
	~~Suppose that~~
	~~:<math>(F,m):(\mathcal C,\otimes,~~I)\to ~~(\mathcal D,\bullet,J)</math>~~
	is a ~~lax monoidal functor such that the underlying functor <math>F:\mathcal C\to\mathcal D</math> has a right adjoint <math>G:\mathcal D\to\mathcal C</math>~~. ~~This adjuction lifts~~ to ~~a monoidal adjuction <math>(F,~~m)<~~/math~~>⊣<~~math~~>~~(G,n)<~~/~~math> if and only if the lax monoidal functor <math>(F,m)<~~/~~math> is strong~~.

	~~== See also ==~~
	* Every monoidal adjunction <math>(F,m)</~~math>⊣<math>(G,n)<~~/~~math> defines a [[monoidal monad]] <math>G\circ F<~~/~~math>.~~

	~~[[Category:Adjoint functors]]~~
	~~[[Category:Monoidal categories]~~]

en>Mark viking: Added wl, move wl to first instance

2013-11-17T05:03:54Z

Added wl, move wl to first instance

← Older revision		Revision as of 07:03, 17 November 2013
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	~~I would like to introduce myself to you~~, I ~~am Andrew~~ and ~~my wife doesn~~'~~t like it at all. Distributing production is where my main earnings comes from and it~~'s ~~some thing~~ I ~~truly appreciate. My spouse~~ and ~~accurate [http~~:/~~/www.publicpledge.com/blogs/post/7034 good psychic~~] ~~readings~~ ([~~http~~://~~myfusionprofits~~.~~com~~/~~groups~~/~~find-out-about-self-improvement-tips-here/ http~~:/~~/myfusionprofits~~.~~com~~/~~groups~~/~~find-out-about-self-improvement-tips-here/]) I reside in Mississippi~~ and ~~I adore every day residing right here. One of~~ the ~~extremely best things in the globe for him~~ is ~~doing ballet and he'll be starting something else along with it~~.<br><br>~~Also visit my web blog - phone psychic~~ ([~~http:~~/~~/netwk~~.~~hannam.ac.kr/xe/data_2/85669 see it here~~])		{{Unreferenced\|date=March 2009}}
			Suppose that <math>(\mathcal C,\otimes,I)</math> and <math>(\mathcal D,\bullet,J)</math> are two [[monoidal category\|monoidal categories]]. A '''monoidal adjunction''' between two [[lax monoidal functor]]s
			:<math>(F,m):(\mathcal C,\otimes,I)\to (\mathcal D,\bullet,J)</math> and <math>(G,n):(\mathcal D,\bullet,J)\to(\mathcal C,\otimes,I)</math>
			is an [[Adjoint functors\|adjunction]] <math>(F,G,\eta,\varepsilon)</math> between the underlying functors, such that the [[natural transformation]]s
			:<math>\eta:1_{\mathcal C}\Rightarrow G\circ F</math> and <math>\varepsilon:F\circ G\Rightarrow 1_{\mathcal D}</math>
			are [[monoidal natural transformation]]s.

			== Lifting adjunctions to monoidal adjunctions ==
			Suppose that
			:<math>(F,m):(\mathcal C,\otimes,I)\to (\mathcal D,\bullet,J)</math>
			is a lax monoidal functor such that the underlying functor <math>F:\mathcal C\to\mathcal D</math> has a right adjoint <math>G:\mathcal D\to\mathcal C</math>. This adjuction lifts to a monoidal adjuction <math>(F,m)</math>⊣<math>(G,n)</math> if and only if the lax monoidal functor <math>(F,m)</math> is strong.

			== See also ==
			* Every monoidal adjunction <math>(F,m)</math>⊣<math>(G,n)</math> defines a [[monoidal monad]] <math>G\circ F</math>.

			[[Category:Adjoint functors]]
			[[Category:Monoidal categories]]

en>Braincricket: Typo fixing, typos fixed: well-known → well known using AWB (8062)

2012-06-22T02:50:30Z

Typo fixing, typos fixed: well-known → well known using AWB (8062)

New page

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