最終更新日：2022/12/07
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(category theory) A category 𝒞 with a bifunctor ⊗:𝒞⨯𝒞→𝒞 which may be called tensor product, an associativity isomorphism 𝛼_(A,B,C):(A⊗B)⊗C≃A⊗(B⊗C), an object I which may be called tensor unit, a left unit natural isomorphism 𝜆_A:I⊗A≃A, a right unit natural isomorphism 𝜌_A:A⊗I≃A, and some coherence conditions
(pentagon and triangle commutative diagrams for those isomorphisms).
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元となった辞書の項目
monoidal category
noun
(category
theory)
A
category
𝒞
with
a
bifunctor
⊗:𝒞⨯𝒞→𝒞
which
may
be
called
tensor
product,
an
associativity
isomorphism
𝛼_(A,B,C):(A⊗B)⊗C≃A⊗(B⊗C),
an
object
I
which
may
be
called
tensor
unit,
a
left
unit
natural
isomorphism
𝜆_A:I⊗A≃A,
a
right
unit
natural
isomorphism
𝜌_A:A⊗I≃A,
and
some
"coherence
conditions"
(pentagon
and
triangle
commutative
diagrams
for
those
isomorphisms).
意味（1）
(category
theory)
A
category
𝒞
with
a
bifunctor
⊗:𝒞⨯𝒞→𝒞
which
may
be
called
tensor
product,
an
associativity
isomorphism
𝛼_(A,B,C):(A⊗B)⊗C≃A⊗(B⊗C),
an
object
I
which
may
be
called
tensor
unit,
a
left
unit
natural
isomorphism
𝜆_A:I⊗A≃A,
a
right
unit
natural
isomorphism
𝜌_A:A⊗I≃A,
and
some
"coherence
conditions"
(pentagon
and
triangle
commutative
diagrams
for
those
isomorphisms).
