Sub-APS

From Apstheory

Revision as of 08:10, 9 March 2012 (edit) 192.162.19.21 (Talk) (ZKQWhn I loved your article.Really thank you! Will read on...) ← Previous diff		Current revision as of 18:55, 14 December 2013 (edit) (undo) 37.233.27.142 (Talk) (AC5gQV I cannot thank you enough for the blog article.Really looking forward to read more. Fantastic.)
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	{{basicapsdef}}		{{basicapsdef}}
-	==Definition==	+	AC5gQV I cannot thank you enough for the blog article.Really looking forward to read more. Fantastic.
-	Let <math>(G,\\Phi)</math> be an [[APS]] over a monoidal concrete category. Then a sub-APS of <math>(G,\\Phi)</math> associates to each <math>n</math> a subobject <math>H_n</math> of <math>G_n</math> such that the restriction of <math>\\Phi_{m,n}</math> to <math>H_m</math> &times; <math>H_n</math> takes it inside <math>H_{m+n}</math>.	+
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-	Thus we can view <math>(H,\\Phi)</math> as an APS in its own right (note that since the associativity condition is satisfied for the block concatenation on <math>G</math>, it is also satisfied for the block concatenation on <math>H</math>.	+
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-	Since the <math>\\Phi</math> is understood for the sub-APS, we may omit it and simply say that <math>H</math> is a sub-APS of <math>G</math>.	+
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-	ZKQWhn I loved your article.Really thank you! Will read on...	+

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Current revision as of 18:55, 14 December 2013

This article gives a basic definition in the APS theory. It is strictly local to the wiki

AC5gQV I cannot thank you enough for the blog article.Really looking forward to read more. Fantastic.