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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
Anders Kock kindly pointed my attention today to remark 7.3.1 in his Synthetic Geometry of Manifolds, which has an observation that goes in the direction of the observation that the jet comonad $J^\infty$ is the base change comonad along the map $X \to \Im X$, i.e. along the coequalizer of the two maps out of the formal neighbourhood of the diagonal.
I have added to the entry a quick remark on this.
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