nLab
magma

A binary operation on a set $S$ is a function from $S\times S$ to $S$. A magma is a set equipped with a binary operation on it.

The term ‘magma’ is from Bourbaki and intends to suggest the fluidity of the concept; special cases include semigroups, quasigroups, groups, and so on. The term ‘groupoid’ is also used, but here that word means something else.

More generally, in any monoidal category $M$, a magma object or magma in $M$ is an object $X$ of $M$ equipped with a morphism $m:X\otimes X\to X$ in $M$. Here the morphism from $X\otimes X$ to $X$ is a binary operation in $M$.