(A o C) o Colimit = (B o C) o Colimit

if known A, B, C and framework of Colimit

can it be said colimit?

Bonus, what are A,B,C? <- this can be not answered

after integration,
result is x^2

f := x^2

we know in the range 5..-5 = 5^2 - (-5)^2 = 0

this example is not good enough, as i can be any number x, -x

if in another example, i use a and b to represent that would like to find

3*a^2 - 3*b^2 = 0, how to find possible a and b?

my example is not good, is there example that a and b are different number, not only in sign

i have a sense that substitution represent associative x*y and x+y

is my understanding correct?

if i change associative property to gcd and lcd,

how to do composition?

if associative is a pair of function, x+y, x*y

does it mean that non associative should also a pair

is it possible replace substitution with two operation x+y and x*y?

How to find inverse function of a multivariable function

for example

f := x^2 + y + z^3

f := x^2 + y^3

a := matrix(...);
b := Convert to hermit matrix from a;
Norm(MatrixMatrixMultiply(b, a), 2) = Norm(a,2)^2

i have tried, but not exactly equal
Norm(MatrixMatrixMultiply(b, a), 2) = 0.01
Norm(a,2)^2 = 0.1

Guess what matrix a is?