Definitionen
1.NounA 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).