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Question on Turaev's paper about axioms for topological quantum field theory

What are D-branes (in a topological field theory)?Atiyah's definitions of Topological Quantum Field TheoryPrerequisites for ‘Quantum field theory and representation theory: a sketch’ [arXiv:hep-th/0206135](Topological quantum field theory) identifying objects of cobordism categoryTopological Quantum Field theoriesLearning roadmap to Topological Quantum Field Theories from a mathematics perspectiveGeometric algebra and quantum field theoryExtended Topological Quantum Field Theory (ETQFT) by Jacob LurieTopological Quantum Field TheoryLiterature recommendation: Algebraic Quantum Field Theory

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$begingroup$

I am currently reading Turaev's paper Axioms for topological quantum field theory.

In couple of place, there is a paraphrase "... is natural with respect to $mathfrak{U}$-homeomorphism" and I don't really understand what does it mean. One is in the definition of self-dual modular functor.

It says system of bilinear pairing is natural with respect to $mathfrak{U}$-homeomorphism and the other is in the definition of cobordism. It says gluing is natural with respect to $mathfrak{U}$-homeomorphism. It seem like that paraphrase is something I should get used to before jumping into Turaev's papers.

If so, a book suggestion would be very helpful. If not, can someone explain what Turaev means by the paraphrase.

reference-request category-theory mathematical-physics quantum-field-theory topological-quantum-field-theory

share|cite|improve this question

edited Mar 11 at 20:01

dantopa

6,64942245

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There's a category of such homeomorphisms. Do you know what a natural transformation is?
  $endgroup$
  – Kevin Carlson
  Jul 11 '18 at 16:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I know what natural transformation but i don't really know how to see any entitiy as a functor in that context.
  $endgroup$
  – erolbarut
  Jul 11 '18 at 18:40
  

  
  
  
  

add a comment | 

1

1

$begingroup$

I am currently reading Turaev's paper Axioms for topological quantum field theory.

In couple of place, there is a paraphrase "... is natural with respect to $mathfrak{U}$-homeomorphism" and I don't really understand what does it mean. One is in the definition of self-dual modular functor.

It says system of bilinear pairing is natural with respect to $mathfrak{U}$-homeomorphism and the other is in the definition of cobordism. It says gluing is natural with respect to $mathfrak{U}$-homeomorphism. It seem like that paraphrase is something I should get used to before jumping into Turaev's papers.

If so, a book suggestion would be very helpful. If not, can someone explain what Turaev means by the paraphrase.

reference-request category-theory mathematical-physics quantum-field-theory topological-quantum-field-theory

share|cite|improve this question

edited Mar 11 at 20:01

dantopa

6,64942245

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  There's a category of such homeomorphisms. Do you know what a natural transformation is?
  $endgroup$
  – Kevin Carlson
  Jul 11 '18 at 16:54
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I know what natural transformation but i don't really know how to see any entitiy as a functor in that context.
  $endgroup$
  – erolbarut
  Jul 11 '18 at 18:40
  

  
  
  
  

add a comment | 

$begingroup$

I am currently reading Turaev's paper Axioms for topological quantum field theory.

In couple of place, there is a paraphrase "... is natural with respect to $mathfrak{U}$-homeomorphism" and I don't really understand what does it mean. One is in the definition of self-dual modular functor.

It says system of bilinear pairing is natural with respect to $mathfrak{U}$-homeomorphism and the other is in the definition of cobordism. It says gluing is natural with respect to $mathfrak{U}$-homeomorphism. It seem like that paraphrase is something I should get used to before jumping into Turaev's papers.

If so, a book suggestion would be very helpful. If not, can someone explain what Turaev means by the paraphrase.

reference-request category-theory mathematical-physics quantum-field-theory topological-quantum-field-theory

share|cite|improve this question

edited Mar 11 at 20:01

dantopa

6,64942245

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406

$endgroup$

share|cite|improve this question

edited Mar 11 at 20:01

dantopa

6,64942245

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406

share|cite|improve this question

edited Mar 11 at 20:01

dantopa

6,64942245

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406

edited Mar 11 at 20:01

dantopa

6,64942245

edited Mar 11 at 20:01

dantopa

6,64942245

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406

asked Jul 11 '18 at 14:00

erolbaruterolbarut

406