Monism is a philosophical position which states that there is only one valid approach to a particular field. This contrasts with pluralism, which states that there are multiple equally valid approaches to a particular field.
In the context of the foundations of mathematics, monism states that there is only a one valid approach to the foundations of mathematics. Traditionally, the mathematical status quo regarded the material set theory of ZFC as the one valid approach to the foundations of mathematcs. Some category theorists take the categorical set theory of ETCS as the one valid approach to the foundations of mathematics, while some type theorists take Martin-Löf type theory or cubical type theory to be the one valid approach to the foundations of mathematics.
On the failure of monism in set theory:
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