leanprover-community / mathlib3

Lean 3's obsolete mathematical components library: please use mathlib4
https://leanprover-community.github.io/lean3
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Unify (or at least connect) `order_hom` and `rel_hom` #5525

Open awainverse opened 3 years ago

awainverse commented 3 years ago

order_hom is essentially the same as a rel_hom between two instances of . One of two things should happen:

YaelDillies commented 2 years ago

Now that I worked a lot on order homs (building the order categories), I feel like the first option is the wrong one. Building on top of rel_hom means that we don't have custom field names and we can't extend order_hom. Instead, we must extend @rel_hom α β (≤) (≤).

I will work on redefining order_embedding and order_iso away from rel_embedding and rel_iso.

I'm not sure we need the second option much either, because rel_homs are used so little in mathlib. But maybe one day we will want to translate between orders and graphs?