From 1cd47be72cf18a6b82b064afb9be853fd8832350 Mon Sep 17 00:00:00 2001 From: Smaug123 Date: Sat, 13 Apr 2024 18:16:29 +0100 Subject: [PATCH] Comment about squashing --- hugo/content/posts/2024-04-13-yoneda.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/hugo/content/posts/2024-04-13-yoneda.md b/hugo/content/posts/2024-04-13-yoneda.md index 187fa46..3726f71 100644 --- a/hugo/content/posts/2024-04-13-yoneda.md +++ b/hugo/content/posts/2024-04-13-yoneda.md @@ -27,7 +27,7 @@ Recall what the functor laws in this context are: Note what we're *not* requiring of our instantiations: that they're somehow "fully preserving all the structure". If \\(\mathcal{C}\\) has two objects \\(A\\) and \\(B\\), we're perfectly happy to instantiate both of them to the same type, as long as all the arrows keep composing correctly. -In particular, every category has a trivial instantiation to the universe where there's only one set \\(\emptyset\\), and only one arrow \\(\mathrm{id} : \emptyset \to \emptyset\\). +In particular, for example, our instantiation might squash away arbitrarily much of the category's structure: every category has a trivial instantiation to the universe where there's only one set \\(\emptyset\\), and only one arrow \\(\mathrm{id} : \emptyset \to \emptyset\\). # Homomorphisms between diagrams