Map (higher-order function) - Revision history

en>Stesmo: Reverted 1 edit by Raymond Swindon identified as test/vandalism using STiki

2015-01-02T23:59:49Z

Reverted 1 edit by Raymond Swindon identified as test/vandalism using STiki

← Older revision		Revision as of 01:59, 3 January 2015
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	~~Hello~~ and ~~welcome~~. ~~My name is Figures Wunder. His spouse doesn~~'t ~~like~~ it ~~the way he does but what he~~ really ~~likes doing is to do aerobics and he's been performing it for fairly a whilst~~. ~~Puerto Rico is exactly where he~~ and ~~his wife~~ live. ~~Managing individuals is his profession~~.<br><br>~~Feel free to surf to~~ my ~~weblog~~ [http://~~xrambo~~.com/~~blog~~/~~191590 home std test kit~~]		Hi there, I am Alyson Pomerleau and I think it sounds quite great when you say it. I am really fond of handwriting but I can't make it my occupation really. My spouse and I live in Kentucky. I am presently a travel agent.<br><br>Also visit my site: [http://mybrandcp.com/xe/board_XmDx25/107997 clairvoyant psychic]

2607:F140:400:1016:FCA5:E86D:BBAA:13CA at 20:28, 25 February 2014

2014-02-25T20:28:51Z

← Older revision		Revision as of 22:28, 25 February 2014
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	~~In [[mathematics]], a [[category (category theory)\|category]]~~ is '~~''distributive''' if~~ it ~~has finite [[product (category theory)\|product]]s~~ and ~~finite [[coproduct (category theory)\|coproduct]]~~s ~~such that~~ for ~~every choice of objects <math>A,B,C</math>, the canonical map~~		Hello and welcome. My name is Figures Wunder. His spouse doesn't like it the way he does but what he really likes doing is to do aerobics and he's been performing it for fairly a whilst. Puerto Rico is exactly where he and his wife live. Managing individuals is his profession.<br><br>Feel free to surf to my weblog [http://xrambo.com/blog/191590 home std test kit]

	~~: <math>[\mathit{id}_A \times\iota_1, \mathit{id}_A \times\iota_2] : A\times B + A\times C\to A\times(B+C)</math>~~

	is ~~an [[isomorphism]],~~ and ~~for all objects <math>A</math>, the canonical map <math>0 \to A\times 0</math>~~ is ~~an isomorphism~~. ~~Equivalently. if for every object~~ <~~math~~>A<~~/math~~> ~~the functor <math>A\times -<~~/~~math> preserves coproducts up to isomorphisms <math>f<~~/~~math>~~.~~<ref>{{cite book\|last=Taylor\|first=Paul\|title=Practical Foundations of Mathematics\|publisher=Cambridge University Press\|year=1999\|page=275}}<~~/~~ref> It follows that <math>f</math> and aforementioned canonical maps are equal for each choice of objects.~~

	~~In particular, if the functor <math>A\times -<~~/math> has a right [[adjoint functors\|adjoint]] (i.e., if the category is [[cartesian closed category\|cartesian closed]]), it necessarily preserves all colimits, and thus any cartesian closed category with finite coproducts (i.e., any [[bicartesian closed category]]) is distributive.

	~~For example, '''[[Category of sets\|Set]]''' is distributive, while '''[[category of groups\|Grp]]''' is not, even though it has both products and coproducts.~~

	~~==References==~~
	~~{{reflist}}~~

	~~[[Category:Category theory]~~]


	~~{{categorytheory-stub}}~~

98.66.52.233: remove redundant redundancy

2014-01-12T19:10:46Z

remove redundant redundancy

← Older revision		Revision as of 21:10, 12 January 2014
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	~~Hello and welcome. My name~~ is ~~Numbers Wunder. To collect coins is a thing that I~~'~~m totally addicted to. For many years he~~'s ~~been residing in North Dakota~~ and ~~his family members loves it~~. ~~Since she was eighteen she's been working as a meter reader but she's always wanted her personal company~~.<br><br>~~Feel free~~ to ~~surf to my~~ page ... [~~http://www~~.~~dailyroads~~.~~com/profile_info~~.~~php?ID~~=~~2363798 home std test~~]		In [[mathematics]], a [[category (category theory)\|category]] is '''distributive''' if it has finite [[product (category theory)\|product]]s and finite [[coproduct (category theory)\|coproduct]]s such that for every choice of objects <math>A,B,C</math>, the canonical map

			: <math>[\mathit{id}_A \times\iota_1, \mathit{id}_A \times\iota_2] : A\times B + A\times C\to A\times(B+C)</math>

			is an [[isomorphism]], and for all objects <math>A</math>, the canonical map <math>0 \to A\times 0</math> is an isomorphism. Equivalently. if for every object <math>A</math> the functor <math>A\times -</math> preserves coproducts up to isomorphisms <math>f</math>.<ref>{{cite book\|last=Taylor\|first=Paul\|title=Practical Foundations of Mathematics\|publisher=Cambridge University Press\|year=1999\|page=275}}</ref> It follows that <math>f</math> and aforementioned canonical maps are equal for each choice of objects.

			In particular, if the functor <math>A\times -</math> has a right [[adjoint functors\|adjoint]] (i.e., if the category is [[cartesian closed category\|cartesian closed]]), it necessarily preserves all colimits, and thus any cartesian closed category with finite coproducts (i.e., any [[bicartesian closed category]]) is distributive.

			For example, '''[[Category of sets\|Set]]''' is distributive, while '''[[category of groups\|Grp]]''' is not, even though it has both products and coproducts.

			==References==
			{{reflist}}

			[[Category:Category theory]]


			{{categorytheory-stub}}

188.174.191.191: wrong link

2012-09-02T00:43:06Z

wrong link

New page

Hello and welcome. My name is Numbers Wunder. To collect coins is a thing that I'm totally addicted to. For many years he's been residing in North Dakota and his family members loves it. Since she was eighteen she's been working as a meter reader but she's always wanted her personal company.<br><br>Feel free to surf to my page ... [http://www.dailyroads.com/profile_info.php?ID=2363798 home std test]