>>82273137
I called it "another" multiplication, but I guess that is a bit misleading. The best term would be "dual". It's not a multiplicative inverse like division, instead you are reversing arows in a diagram. Basically, in multiplication you take two inputs and give one output. In comultiplication, you take one input and give "two outputs", which is really just one in the form of a tensor product (which you can naively think as a cartesian product). For example, in multiplication you take 3 and 4 and are given 12, while in comultiplication you can, for example, take 3 and can be given "3 tensor 3". It's like if you were cloning the number into another coordinate. But algebraically, it behaves a lot like multiplication.
This is a very rough sketch, I'm currently studying this, but I think explaining things helps me understand them better, so if you have any aditional questions feel free to ask.