Spectral space - Revision history

46.143.248.50: /* Definition */

2014-12-16T07:32:51Z

Definition

← Older revision		Revision as of 09:32, 16 December 2014
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	~~In [[mathematics]], a '''bicategory'''~~ is ~~a concept in [[category theory]] used~~ to ~~extend the notion of [[Category (mathematics)\|category]] to handle the cases where the composition of morphisms is not (strictly) [[associative]],~~ but ~~only associative~~ ''[[up ~~to]]~~'~~' an isomorphism~~. ~~The notion was introduced in 1967 by~~ [[~~Jean Bénabou]~~].		Adrianne is what you is going to call me but We all don't like when individuals use my full full name. What I cherish doing is fish and I'll be opening up something else along along with. Filing would be my day job but but soon I'll getting on my own. [http://www.reddit.com/r/howto/search?q=Vermont Vermont] also has always been my tough to adapt place and I will have everything that I desire here. Go to my [https://www.gov.uk/search?q=website website] to find out more: http://prometeu.net<br><br>

	~~Formally, a bicategory '''B''' consists of~~:		Also visit my blog [http://prometeu.net Clash of clans cheats]
	* objects ''a'', ''b''... called ''0-cells'';
	* morphisms ''f'', ''g'', ... with fixed source and target objects called ''1-cells'';
	* "morphisms between morphisms" ρ, σ... with fixed source and target morphisms (which should have themselves the same source and the same target), called ''2-cells'';
	~~with some more structure:~~
	* given two objects ''a'' and ''b'' there is a category '''B'''(''a'', ''b'') whose objects are the 1-cells and morphisms are the 2-cells, the composition in this category is called ''vertical composition'';
	* given three objects ''a'', ''b'' and ''c'', there is a bifunctor <math>*:\mathbf{B}(b,c)\times\mathbf{B}(a,b)\to\mathbf{B}(a,c)</~~math> called ''horizontal composition''.~~
	~~The horizontal composition is required to be associative up to a natural isomorphism α between morphisms <math>h(gf)<~~/~~math> and <math>(hg)f</math>. Some more coherence axioms, similar to those needed for [[monoidal category\|monoidal categories]], are moreover required to hold.~~

	~~Bicategories may be considered as a weakening of the definition of [[2-categories]]~~. ~~A similar process for 3-categories leads to [[tricategory\|tricategories]], and more generally to [[weak n-category\|weak ''n''-categories]] for [[n-category\|''n''-categories]].~~

	~~== References ==~~
	* J. Bénabou. "Introduction to bicategories, part I". In ''Reports of ~~the Midwest Category Seminar'', Lecture Notes in Mathematics 47, pages 1-77. Springer, 1967.~~

	~~[[Category:Higher category theory]~~]

159.149.107.58: /* Spectral maps */

2013-12-02T10:22:49Z

Spectral maps

← Older revision		Revision as of 12:22, 2 December 2013
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	~~Let~~'~~s look an actual registry scan plus~~ a ~~few~~ of ~~what you~~'~~ll see when you do 1 on a computer~~. ~~This test~~ was ~~performed on~~ a ~~computer which was not working as it should~~, ~~running at slow speed and having certain issues with freezing up~~.~~<br><br>Firstly~~, ~~we should employ your Antivirus or safety tool plus run a scan on your computer~~. ~~It is possible which a computer is infected with virus or malware which slows down your computer~~. ~~If there is nothing found inside the scanning report, it could be the RAM which cause the issue~~.~~<br><br>System tray icon makes it simple to launch the system~~ and ~~displays~~ "~~clean~~" ~~status or the amount of errors inside the last scan~~. ~~The ability to obtain plus remove the Invalid class keys and shell extensions is regarded as the primary advantages of the program~~. ~~That is not usual function for the different Registry Cleaners~~. ~~Class keys plus shell extensions~~ which ~~are not functioning may seriously slow down~~ the ~~computer. RegCure scans to find invalid entries plus delete them.<br><br>Paid registry products found on~~ the ~~other hand~~, ~~I have found~~, are ~~often inexpensive. They offer usual, free updates or at least cheap updates. This follows considering~~ the ~~software manufacturer requirements to ensure their product is best in staying ahead of its competitors.<br><br>Use a [http://bestregistrycleanerfix.com/tune~~-up-~~utilities tuneup utilities 2014]. This can search your Windows registry for three kinds of keys which will really hurt PC performance. These are: duplicate, missing~~, ~~and corrupted.<br><br>Files with all~~ the ~~DOC extension are equally susceptible to viruses, however~~ this is ~~solved by superior antivirus programs. Another problem is the fact that .doc files may be corrupted~~, ~~unreadable or damaged due to spyware~~, ~~adware, plus malware. These situations usually avoid consumers from correctly opening DOC files. This~~ is ~~when powerful registry cleaners become worthwhile.~~<br>~~<br>It is important that you remove obsolete registry entries from the program regularly~~, ~~if you want your program~~ to ~~run faster~~, ~~that is. If you don~~'~~t keep a registry clean, a time usually come when your program will stop working altogether~~. ~~Next, your only option~~ is to ~~reformat the hard drive plus start over!~~<br><br>~~A registry cleaner is a program that cleans the registry~~. ~~The Windows registry constantly gets flooded with junk information~~, ~~info that has not been removed from uninstalled programs~~, ~~erroneous file association plus other computer-misplaced entries~~. ~~These clean small system software tools are very well-known nowadays plus you will find very~~ a ~~few advantageous ones found on~~ the ~~Internet~~. ~~The superior ones provide you way~~ to ~~maintain~~, ~~clean~~, ~~update~~, ~~backup~~, ~~plus scan the System Registry~~. ~~When it finds supposedly unwanted ingredients inside it~~, ~~the registry cleaner lists them plus recommends the consumer to delete or repair these orphaned entries plus corrupt keys~~.		In [[mathematics]], a '''bicategory''' is a concept in [[category theory]] used to extend the notion of [[Category (mathematics)\|category]] to handle the cases where the composition of morphisms is not (strictly) [[associative]], but only associative ''[[up to]]'' an isomorphism. The notion was introduced in 1967 by [[Jean Bénabou]].

			Formally, a bicategory '''B''' consists of:
			* objects ''a'', ''b''... called ''0-cells'';
			* morphisms ''f'', ''g'', ... with fixed source and target objects called ''1-cells'';
			* "morphisms between morphisms" ρ, σ... with fixed source and target morphisms (which should have themselves the same source and the same target), called ''2-cells'';
			with some more structure:
			* given two objects ''a'' and ''b'' there is a category '''B'''(''a'', ''b'') whose objects are the 1-cells and morphisms are the 2-cells, the composition in this category is called ''vertical composition'';
			* given three objects ''a'', ''b'' and ''c'', there is a bifunctor <math>*:\mathbf{B}(b,c)\times\mathbf{B}(a,b)\to\mathbf{B}(a,c)</math> called ''horizontal composition''.
			The horizontal composition is required to be associative up to a natural isomorphism α between morphisms <math>h(gf)</math> and <math>(hg)f</math>. Some more coherence axioms, similar to those needed for [[monoidal category\|monoidal categories]], are moreover required to hold.

			Bicategories may be considered as a weakening of the definition of [[2-categories]]. A similar process for 3-categories leads to [[tricategory\|tricategories]], and more generally to [[weak n-category\|weak ''n''-categories]] for [[n-category\|''n''-categories]].

			== References ==
			* J. Bénabou. "Introduction to bicategories, part I". In ''Reports of the Midwest Category Seminar'', Lecture Notes in Mathematics 47, pages 1-77. Springer, 1967.

			[[Category:Higher category theory]]

en>Helpful Pixie Bot: ISBNs (Build KE)

2012-05-09T07:28:58Z

ISBNs (Build KE)

New page

Let's look an actual registry scan plus a few of what you'll see when you do 1 on a computer. This test was performed on a computer which was not working as it should, running at slow speed and having certain issues with freezing up. Firstly, we should employ your Antivirus or safety tool plus run a scan on your computer. It is possible which a computer is infected with virus or malware which slows down your computer. If there is nothing found inside the scanning report, it could be the RAM which cause the issue. System tray icon makes it simple to launch the system and displays "clean" status or the amount of errors inside the last scan. The ability to obtain plus remove the Invalid class keys and shell extensions is regarded as the primary advantages of the program. That is not usual function for the different Registry Cleaners. Class keys plus shell extensions which are not functioning may seriously slow down the computer. RegCure scans to find invalid entries plus delete them. Paid registry products found on the other hand, I have found, are often inexpensive. They offer usual, free updates or at least cheap updates. This follows considering the software manufacturer requirements to ensure their product is best in staying ahead of its competitors. Use a [http://bestregistrycleanerfix.com/tune-up-utilities tuneup utilities 2014]. This can search your Windows registry for three kinds of keys which will really hurt PC performance. These are: duplicate, missing, and corrupted. Files with all the DOC extension are equally susceptible to viruses, however this is solved by superior antivirus programs. Another problem is the fact that .doc files may be corrupted, unreadable or damaged due to spyware, adware, plus malware. These situations usually avoid consumers from correctly opening DOC files. This is when powerful registry cleaners become worthwhile. It is important that you remove obsolete registry entries from the program regularly, if you want your program to run faster, that is. If you don't keep a registry clean, a time usually come when your program will stop working altogether. Next, your only option is to reformat the hard drive plus start over! A registry cleaner is a program that cleans the registry. The Windows registry constantly gets flooded with junk information, info that has not been removed from uninstalled programs, erroneous file association plus other computer-misplaced entries. These clean small system software tools are very well-known nowadays plus you will find very a few advantageous ones found on the Internet. The superior ones provide you way to maintain, clean, update, backup, plus scan the System Registry. When it finds supposedly unwanted ingredients inside it, the registry cleaner lists them plus recommends the consumer to delete or repair these orphaned entries plus corrupt keys.