圏論 3分(?) クッキング
TRANSCRIPT
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30
wikipedia,https://ja.wikipedia.org/wiki/_()
()
: (@aiya_000): C#
: Haskell
Twitter()
C - X, Y, Z (X,Y,ZC)
- (X, Y) f : X -> Y
- X idX : X -> X
X, Y, Zf : X -> YidX : X -> XidY : Y -> Y
C (X,Y,Z)
f : X -> Y, g : Y -> Z
g f : X -> Z
f : X -> Yg : Y -> Z () (g f) : X -> Z
fXdomain()
fYcodomain()gY, Z
f : X -> Yg : Y -> Z () (g f) : X -> Z
(h g) f = h (g f) ()
idY f = f idX = f
f : X -> Yg : Y -> Zh : Z -> VidX : X -> XidY : Y -> Y
()
()
Grp - ()
GrpGrp'
Z
Y
A(A)
X
X'
B(B)
Y'
Z'
f(f):A -> B
()
Grp - ()
ABf:A -> B
GrpGrp'
2C,D
F:C -> DC,DCXDF(X)
Cf : X -> Y
DF(f) : F(X) -> F(Y)
CXDF(X)
Cf : X -> Y DF(f): F(X) -> F(Y)
XY
f
F(X)F(Y)
F(f)
FC
D
CD=
CD=
XY
f
F(X)F(Y)
F(f)
FC
D
CDXC F(X)D
YC F(Y)D
XY
f
F(X)F(Y)
F(f)
C
D
CD2XCF(idX) = idF(X)
C
D
XidX
idF(X)
F(X)
XC F(idX) = idF(X)idX C
idF(X) D
F(idX) D
C
D
XidX
idF(X)
F(X)
XC F(idX) = idF(X)
C
D
XidX
idF(X)
F(X)
CD2f:X->Y, g:Y->Z F(gf) = F(g) F(f)
\ Zunko has gone to the heaven /
C
XYZ
f
g
gf
D
XYZ
F(f)
F(g)
F(gf)= F(g)F(f)
f:X->Y, g:Y->Z F(gf) = F(g) F(f)
\ Zunko has gone to the heaven /
C
XYZ
f
g
gf
D
XYZ
F(f)
F(g)
F(gf)= F(g)F(f)
G : C -> C
C
XYZ
f
g
G : C -> C
owari !