Yoneda Lemma in Double Categories

Automated excerpt

And without presheaves, we can’t talk about the Yoneda lemma — the workhorse of category theory. Overview To translate the Yoneda construction into the language of double categories, we need to define an object (a 0-cell) of presheaves and a Yoneda vertical arrow (1-cell) — the Yoneda embedding. It lets us classify horizontal arrows using vertical arrows . Yoneda Embedding We can now ask the question: What is the classifying arrow for the simplest horizontal arrow: the unit arrow? A functor from such a category selects an object in the target category.

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