"an X is just a Y" is a common turn of phrase in mathematical writing. It means that Xs and Ys are the same thing, whereas "an X is a Y" may, depending on conte

"an X is just a Y" is a common turn of phrase in mathematical writing. It means that Xs and Ys are the same thing, whereas "an X is a Y" may, depending on context, mean only that every X is a Y. A human is a mammal, but a human is not just a mammal. The original quote (from Categories for the Working Mathematician) is: > All told, a monad in X is just a monoid in the category of endofunctors of X, with product × replaced by composition of endofunctors and unit set by the identity endofunctor.