Name convention for functor and natural transformation composition

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If there are functors $H: D to C; F,G: C to D$ and $K: B to C$ and a natural transformation $alpha: F xrightarrow. G$ then we can construct 2 new natural transformations:



Aka "left composition"
$$H alpha : H F xrightarrow. H G $$
and "right composition"
$$ alpha K : F K xrightarrow. G K $$



I was not able to find the naming convention for these ones and called them as left and right compositions but not sure that there are correct namings. Could anybody help me in the finding correct ones?










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    If there are functors $H: D to C; F,G: C to D$ and $K: B to C$ and a natural transformation $alpha: F xrightarrow. G$ then we can construct 2 new natural transformations:



    Aka "left composition"
    $$H alpha : H F xrightarrow. H G $$
    and "right composition"
    $$ alpha K : F K xrightarrow. G K $$



    I was not able to find the naming convention for these ones and called them as left and right compositions but not sure that there are correct namings. Could anybody help me in the finding correct ones?










    share|cite|improve this question























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      If there are functors $H: D to C; F,G: C to D$ and $K: B to C$ and a natural transformation $alpha: F xrightarrow. G$ then we can construct 2 new natural transformations:



      Aka "left composition"
      $$H alpha : H F xrightarrow. H G $$
      and "right composition"
      $$ alpha K : F K xrightarrow. G K $$



      I was not able to find the naming convention for these ones and called them as left and right compositions but not sure that there are correct namings. Could anybody help me in the finding correct ones?










      share|cite|improve this question













      If there are functors $H: D to C; F,G: C to D$ and $K: B to C$ and a natural transformation $alpha: F xrightarrow. G$ then we can construct 2 new natural transformations:



      Aka "left composition"
      $$H alpha : H F xrightarrow. H G $$
      and "right composition"
      $$ alpha K : F K xrightarrow. G K $$



      I was not able to find the naming convention for these ones and called them as left and right compositions but not sure that there are correct namings. Could anybody help me in the finding correct ones?







      category-theory






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      asked Aug 31 at 7:50









      Ivan

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          It's called whiskering; you can show that it is the same as the horizontal composition of $alpha$ with $1_H:HRightarrow H$ (for your "left composition") or with $1_K:KRightarrow K$ (for your "right composition").






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          • Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
            – Ivan
            Aug 31 at 9:00










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          1 Answer
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          active

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          1 Answer
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          active

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          up vote
          2
          down vote



          accepted










          It's called whiskering; you can show that it is the same as the horizontal composition of $alpha$ with $1_H:HRightarrow H$ (for your "left composition") or with $1_K:KRightarrow K$ (for your "right composition").






          share|cite|improve this answer




















          • Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
            – Ivan
            Aug 31 at 9:00














          up vote
          2
          down vote



          accepted










          It's called whiskering; you can show that it is the same as the horizontal composition of $alpha$ with $1_H:HRightarrow H$ (for your "left composition") or with $1_K:KRightarrow K$ (for your "right composition").






          share|cite|improve this answer




















          • Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
            – Ivan
            Aug 31 at 9:00












          up vote
          2
          down vote



          accepted







          up vote
          2
          down vote



          accepted






          It's called whiskering; you can show that it is the same as the horizontal composition of $alpha$ with $1_H:HRightarrow H$ (for your "left composition") or with $1_K:KRightarrow K$ (for your "right composition").






          share|cite|improve this answer












          It's called whiskering; you can show that it is the same as the horizontal composition of $alpha$ with $1_H:HRightarrow H$ (for your "left composition") or with $1_K:KRightarrow K$ (for your "right composition").







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 31 at 8:56









          Arnaud D.

          14.9k52142




          14.9k52142











          • Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
            – Ivan
            Aug 31 at 9:00
















          • Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
            – Ivan
            Aug 31 at 9:00















          Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
          – Ivan
          Aug 31 at 9:00




          Thank you for the link. It is exactly that I need. I also found the same question in stack exchange and most probably the question has to be removed as the dublicate
          – Ivan
          Aug 31 at 9:00

















           

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