Definiciones
1.NounThe act of joining; the thing joined or added.
2.NounThe joining of personal property owned by one to that owned by another.
3.NounThe process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process."The ring obtained after the adjunction of the elements
a
,
b
{\displaystyle a,b}
and
y
{\displaystyle y}
to the ring
R
{\displaystyle R}
may be denoted
R
[
a
,
b
,
y
]
{\displaystyle R[a,b,y]}
.; The field adjunction
Q
(
π
)
{\displaystyle \mathbb {Q} (\pi )}
can be obtained from
Q
{\displaystyle \mathbb {Q} }
by adjoining
π
{\displaystyle \pi }
to
Q
{\displaystyle \mathbb {Q} }
."
4.NounA relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
5.NounA natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.
(formally, given two categories
C
{\displaystyle {\mathcal {C}}}
and
D
{\displaystyle {\mathcal {D}}}
and (covariant) functors
F
:
C
→
D
{\displaystyle F:{\mathcal {C}}\rightarrow {\mathcal {D}}}
and
G
:
D
→
C
{\displaystyle G:{\mathcal {D}}\rightarrow {\mathcal {C}}}
) A natural isomorphism
Φ
:
Hom
C
(
G
⋅
,
⋅
)
→
Hom
D
(
⋅
,
F
⋅
)
{\displaystyle \Phi :\operatorname {Hom} _{\mathcal {C}}(G\cdot ,\cdot )\to \operatorname {Hom} _{\mathcal {D}}(\cdot ,F\cdot )}
(where the hom-functors are understood as bifunctors from
D
op
×
C
{\displaystyle {\mathcal {D}}^{\operatorname {op} }\times {\mathcal {C}}}
to
S
e
t
{\displaystyle \mathbf {Set} }
). See Adjoint functors on Wikipedia.Wikipedia .
6.Noun(formally, given two categories
C
{\displaystyle {\mathcal {C}}}
and
D
{\displaystyle {\mathcal {D}}}
and (covariant) functors
F
:
C
→
D
{\displaystyle F:{\mathcal {C}}\rightarrow {\mathcal {D}}}
and
G
:
D
→
C
{\displaystyle G:{\mathcal {D}}\rightarrow {\mathcal {C}}}
) A natural isomorphism
Φ
:
Hom
C
(
G
⋅
,
⋅
)
→
Hom
D
(
⋅
,
F
⋅
)
{\displaystyle \Phi :\operatorname {Hom} _{\mathcal {C}}(G\cdot ,\cdot )\to \operatorname {Hom} _{\mathcal {D}}(\cdot ,F\cdot )}
(where the hom-functors are understood as bifunctors from
D
op
×
C
{\displaystyle {\mathcal {D}}^{\operatorname {op} }\times {\mathcal {C}}}
to
S
e
t
{\displaystyle \mathbf {Set} }
). See Adjoint functors on Wikipedia.Wikipedia .