frobenius algebras and 2d topological quantum field theories
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Frobenius algebras and 2D topological quantum field theories
Junior Topology Seminar
Mustafa Hajij
Note: All figures used in this file are from the reference mentioned in the last slide.
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Categories
Monoidal Functors
Monoidal Functors
Monoidal Functors
Monoidal categories VS strict monoidal categories
Examples of monoidal categories
Examples of monoidal categories
Examples of monoidal categories
Examples of monoidal categories
Examples of monoidal categories
Oriented cobordism
Oriented cobordism
Equivalent cobordisms
The composition of two cobordism classes
The identity cobordism and invertible cobordisms
The identity cobordism and invertible cobordisms
The Category nCob
n-TQFT
n-TQFT
n-TQFT
n-TQFT
n-TQFT
More category theory
More category theory
More category theory
A Skeleton for 2Cob
A generating set for 2Cob
A generating set for 2Cob
Relations for 2Cob
Relations for 2Cob
Relations for 2Cob
Algebras
Non-degenerate bilinear map
Non-degenerate bilinear map
Associative bilinear map
Frobenius algebras
Frobenius algebras
A Frobenius algebra has a natural coalgebra structure
A Frobenius algebra has a natural coalgebra structure
A Frobenius algebra has a natural coalgebra structure
A Frobenius algebra has a natural coalgebra structure
More relations between maps
More relations between maps
The twist map
The twist map relations
Commutative and co-commutative algebras
Commutative and co-commutative algebras
The main theorem
The main theorem
The main theorem
The main theorem
The main theorem
The main theorem
The main theorem
Ref.
Thank you
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