Linear energy transfer: Difference between revisions

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{{Unreferenced|date=December 2009}}
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Suppose that <math>(\mathcal C,\otimes,I)</math> and <math>(\mathcal D,\bullet, J)</math> are two [[monoidal category|monoidal categories]] and
:<math>(F,m):(\mathcal C,\otimes,I)\to(\mathcal D,\bullet, J)</math> and <math>(G,n):(\mathcal C,\otimes,I)\to(\mathcal D,\bullet, J)</math>
are two [[lax monoidal functor]]s between those categories.
 
A '''monoidal natural transformation'''
:<math>\theta:(F,m)\Rightarrow(G,n)</math>
between those functors is a [[natural transformation]] <math>\theta:F\Rightarrow G</math> between the underlying functors such that the diagrams
:[[Image:Monoidal nat transfo mult.png]] {{spaces|10}} and {{spaces|8}} [[Image:Monoidal nat transfo unit.png]]
commute for every objects <math>A</math> and <math>B</math> of <math>\mathcal C</math>.
 
A '''symmetric monoidal natural transformation''' is a monoidal natural transformation between [[symmetric monoidal functor]]s.
 
{{DEFAULTSORT:Monoidal Natural Transformation}}
[[Category:Monoidal categories]]

Latest revision as of 14:35, 1 October 2014

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