I would say Set Theory. Set theorists keep adding axioms to their Set theory and expect us to do math(such as category theory, mathematical analysis and pretty much all of the known math) withing their formal Axiomatic Set Theory.
Sorry for a late reply but I'm new in this "forum". From experienced, calculus is not a prerequisite for abstract algebra. Many books on abstract algebra presuppose that its readers are familiar with arithmetic among the number systems. They also presuppose that its readers are familiar with...