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AxelBoldt/test
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User:AxelBoldt
So:
Hom
C
(
F
Y
′
,
X
)
→
Φ
Y
′
,
X
Hom
D
(
Y
′
,
G
X
)
↓
Hom
C
(
F
g
,
f
)
↓
Hom
D
(
g
,
G
f
)
Hom
C
(
F
Y
,
X
′
)
→
Φ
Y
,
X
′
Hom
D
(
Y
,
G
X
′
)
{\displaystyle {\begin{array}{ccc}\operatorname {Hom} _{C}(FY',X)&{\xrightarrow {\Phi _{Y',X}}}&\operatorname {Hom} _{D}(Y',GX)\\\\\downarrow {\scriptstyle \operatorname {Hom} _{C}(Fg,f)}&&\downarrow {\scriptstyle \operatorname {Hom} _{D}(g,Gf)}\\\\\operatorname {Hom} _{C}(FY,X')&{\xrightarrow {\Phi _{Y,X'}}}&\operatorname {Hom} _{D}(Y,GX')\\\end{array}}}