It's great to see someone assemble some of their favourite theorems, but, if you have occasion to use these, make sure that you do so with caution. Aside from

It's great to see someone assemble some of their favourite theorems, but, if you have occasion to use these, make sure that you do so with caution. Aside from some typos ('Perseval' for 'Parseval') and some curiosities (stating on p. 3 that the cardinalities of a set and its power set are different, which is true; but why not say that the latter is larger?), I noticed a wrong statement on p.7: assuming that to 'extend' a monoid to a group is to realise it as a submonoid of a larger monoid that is also a group, this cannot be done in general. (For example, the 'min-monoid' whose objects are the natural numbers, and in which the product of two natural numbers is their minimum, does not embed in a group because it obeys no cancellative law.) What is true is that, for every commutative monoid, there is a universal homomorphism from that monoid to a group, in the sense that all other such homomorphisms factor through it. (In my example, this universal homomorphism is the constant-0 homomorphism to the 0 group.)