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Hard question no context:

Let 𝐶 be a category and 𝑋 an object of 𝐶, take the representable presheaf 𝐶 (−,𝑋) : 𝐶ᵒᵖ → 𝐒𝐞𝐭

What does it mean for another presheaf 𝐹 : 𝐶ᵒᵖ → 𝐒𝐞𝐭 to be a monad relative to 𝐶 (−,𝑋) ?

That's a big generalisation of the common setting of a monad relative to the inclusion 𝐅𝐢𝐧𝐒𝐞𝐭 ↪ 𝐒𝐞𝐭, which is represented by the 1-element set