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How to pronounce “monoidal category”
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Pronunciation guide for monoidal category
- Learning goal
- Practice the English pronunciation of monoidal category with real speech in context.
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- Definition summary
- (category theory) A category
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A Deep Dive Into “monoidal category”
Meaning
- [Noun]
- (category theory) A category
- C
- {\displaystyle {\mathcal {C}}}
- with a bifunctor
- ⊗
- :
- C
- ×
- C
- →
- C
- {\displaystyle \otimes :{\mathcal {C}}\times {\mathcal {C}}\rightarrow {\mathcal {C}}}
- which may be called tensor product, an associativity isomorphism
- α
- A
- ,
- B
- ,
- C
- :
- (
- A
- ⊗
- B
- )
- ⊗
- C
- ≃
- A
- ⊗
- (
- B
- ⊗
- C
- )
- {\displaystyle \alpha _{A,B,C}:(A\otimes B)\otimes C\simeq A\otimes (B\otimes C)}
- , an object
- I
- {\displaystyle I}
- which may be called tensor unit, a left unit natural isomorphism
- λ
- A
- :
- I
- ⊗
- A
- ≃
- A
- {\displaystyle \lambda _{A}:I\otimes A\simeq A}
- , a right unit natural isomorphism
- ρ
- A
- :
- A
- ⊗
- I
- ≃
- A
- {\displaystyle \rho _{A}:A\otimes I\simeq A}
- , and some "coherence conditions" (pentagon and triangle commutative diagrams for those isomorphisms).
Practice Nearby Words
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