> Modulo is not an operator,

"operator" is being used as a term of art in programming language design, to describe a symbol used to indicate that an operation should be performed on one or more operands.

https://en.wikipedia.org/wiki/Operator_(computer_programming...

So the "%" symbol is an operator in C and Python, and it is standard usage to describe the operator that performs a mathematical function "X" as the "X operator".

As sibling comments have mentioned, "operator" here is being used in the programming language sense of the word, not the mathematical sense. Using the name "mod" [as in mod(a,n)] or "modulo" for the mapping that takes integers to a particular representative of its equivalence class in Z/nZ ("integers modulo n") doesn't seem like an unreasonable choice to me.

(mod N) is an operator which indicates that the arithmetic in the preceding formula or equation is understood as taking place in a modulo N congruence.

A triple equal sign is usually used for modular equations. That triple equal sign, together with the (mod N) out to the right, constitute an operator.

-1 ≡ 9 (mod 10)

Since it is written as part of the syntax of a formula or equation, and modifies its semantics, it is an operator. Just like d/dx, sigma notation and whatever not.

That's an operator. A map to the quotient.