Finished 1=>2 of theorem 35

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Leon Vatthauer 2023-10-05 14:31:12 +02:00
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@ -203,7 +203,7 @@ We will now show that the following conditions are equivalent:
cond-4 = {! !} cond-4 = {! !}
1⇒2 : cond-1 → cond-2 1⇒2 : cond-1 → cond-2
1⇒2 c-1 X = s-alg-on , {! !} 1⇒2 c-1 X = s-alg-on , (begin ρ ∘ μ.η X ≈⟨ D-universal ⟩ Search-Algebra-on.α s-alg-on ∘ D₁ ρ ∎)
where where
open Coequalizer (coeqs X) renaming (universal to coeq-universal) open Coequalizer (coeqs X) renaming (universal to coeq-universal)
open IsCoequalizer (c-1 X) using () renaming (equality to D-equality; coequalize to D-coequalize; universal to D-universal; unique to D-unique) open IsCoequalizer (c-1 X) using () renaming (equality to D-equality; coequalize to D-coequalize; universal to D-universal; unique to D-unique)