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wikipedia,https://ja.wikipedia.org/wiki/_()

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: (@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 !