remark. Yoneda philosophy [rosiak2022sheaf, sec. 6.6] [tt-002S]

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The Yoneda lemma can be regarded as saying:

To understand an object it suffices to understand all its relationships with other things.

This is similar to the seventeenth-century philosopher Spinoza's idea that what a body is (its “essence”) is inseparable from all the ways that the body can affect (causally influence) and be affected (causally influenced) by other bodies.

The idea of Yoneda is that we can be assured that if a robot wants to learn whether some object \(X\) is the same thing as object \(Y\), it will suffice for it learn whether \[{\cal C}(-, X) \cong {\cal C}(-, Y)\] or, dually, \[{\cal C}(X, -) \cong {\cal C}(Y, -)\] i.e. whether all the ways of probing \(X\) with objects of its environment amount to the same as all the ways of probing \(Y\) with objects of its environment.