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?
category-theory
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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?
category-theory
add a comment |Â
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?
category-theory
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
category-theory
asked Aug 31 at 7:50
Ivan
956
956
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1 Answer
1
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up vote
2
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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").
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
â Ivan
Aug 31 at 9:00
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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").
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
â Ivan
Aug 31 at 9:00
add a comment |Â
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").
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
â Ivan
Aug 31 at 9:00
add a comment |Â
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").
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").
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
â Ivan
Aug 31 at 9:00
add a comment |Â
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
â 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
â 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
â Ivan
Aug 31 at 9:00
add a comment |Â
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