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composition of coreflection and a reflection

0

$begingroup$

What would be the difference between the composition of a coreflection after a reflection (idempotent adjunction?) and the composition of a reflection after a coreflection?

category-theory

share|cite|improve this question

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1

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  $begingroup$
  What are your thoughts?
  $endgroup$
  – Brian
  Apr 1 at 1:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am not a category theory specialist but as I read papers on this, it would seem that to relate categories A and B, some create a category C which is a full subcategory of A and B or a create a category D where A is a full subcategory of D and B is a full subcategory of D. I am not sure of the difference between A as it relates to B in these two modes.
  $endgroup$
  – Albert Lao-an
  Apr 2 at 10:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Note that also the full embedding functors may play a role. Exactly which functors do you want to compose? As stated, a coreflection $Bto C$ after a reflection $Ato B$ would assume $C$ is a coreflective full subcategory of $B$ which is a reflective full subcategory of $A$. I like to draw reflective subcategories as a potato pushed to the right side within a bigger potato.
  $endgroup$
  – Berci
  Apr 2 at 23:25
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am looking more on the Scenario 1, using your example with B as a reflective subcategory of A but with B as a coreflective subcategory of C. A Scenario 2 would be that A is a coreflective subcategory of B and C a reflective subcategory of B. Composition would be A to C in both scenarios.
  $endgroup$
  – Albert Lao-an
  Apr 4 at 15:18
  

  
  
  
  

add a comment | 

0

$begingroup$

What would be the difference between the composition of a coreflection after a reflection (idempotent adjunction?) and the composition of a reflection after a coreflection?

category-theory

share|cite|improve this question

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  What are your thoughts?
  $endgroup$
  – Brian
  Apr 1 at 1:00
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am not a category theory specialist but as I read papers on this, it would seem that to relate categories A and B, some create a category C which is a full subcategory of A and B or a create a category D where A is a full subcategory of D and B is a full subcategory of D. I am not sure of the difference between A as it relates to B in these two modes.
  $endgroup$
  – Albert Lao-an
  Apr 2 at 10:16
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Note that also the full embedding functors may play a role. Exactly which functors do you want to compose? As stated, a coreflection $Bto C$ after a reflection $Ato B$ would assume $C$ is a coreflective full subcategory of $B$ which is a reflective full subcategory of $A$. I like to draw reflective subcategories as a potato pushed to the right side within a bigger potato.
  $endgroup$
  – Berci
  Apr 2 at 23:25
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I am looking more on the Scenario 1, using your example with B as a reflective subcategory of A but with B as a coreflective subcategory of C. A Scenario 2 would be that A is a coreflective subcategory of B and C a reflective subcategory of B. Composition would be A to C in both scenarios.
  $endgroup$
  – Albert Lao-an
  Apr 4 at 15:18
  

  
  
  
  

add a comment | 

$begingroup$

What would be the difference between the composition of a coreflection after a reflection (idempotent adjunction?) and the composition of a reflection after a coreflection?

category-theory

share|cite|improve this question

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1

$endgroup$

share|cite|improve this question

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1

share|cite|improve this question

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1

asked Apr 1 at 0:37

Albert Lao-anAlbert Lao-an

1