julesh
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
Zanzi @ Monoidal Cafe
@julesh very interested in an answer to this!
ohad
@julesh I'd start here: https://arxiv.org/abs/1101.3064
Andy Tonks
@julesh OK maybe I am not understanding the question, but the unit \( \eta\colon \hat C\to F \) is just an element of the set \( FC \) by Yondaa, so that's a start.
julesh
@apt12 Nice
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