I am new to category theory, so apologies if this is obvious.
I recently learned about function equality via composition:
∀c∈C·∀g,h : c→a If f∘g = f∘h ⇒ g=h Where C →g→ A →f→ B & C →h→ A →f→ B
This kind of makes sense, but only for the specific function f. From what I can tell, functions g & h could be considered identical in certain situations, for instance:
g = sin(x)h = i*sin(x)f = abs(x)
Clearly other functions of f could distinguish between the two functions. I'm sure I've misunderstood something but am unsure as to where.
Thanks in advance.