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✨ Finished 1=>2 of theorem 35
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@ -203,7 +203,7 @@ We will now show that the following conditions are equivalent:
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cond-4 = {! !}
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cond-4 = {! !}
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1⇒2 : cond-1 → cond-2
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1⇒2 : cond-1 → cond-2
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1⇒2 c-1 X = s-alg-on , {! !}
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1⇒2 c-1 X = s-alg-on , (begin ρ ∘ μ.η X ≈⟨ D-universal ⟩ Search-Algebra-on.α s-alg-on ∘ D₁ ρ ∎)
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where
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where
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open Coequalizer (coeqs X) renaming (universal to coeq-universal)
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open Coequalizer (coeqs X) renaming (universal to coeq-universal)
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open IsCoequalizer (c-1 X) using () renaming (equality to D-equality; coequalize to D-coequalize; universal to D-universal; unique to D-unique)
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open IsCoequalizer (c-1 X) using () renaming (equality to D-equality; coequalize to D-coequalize; universal to D-universal; unique to D-unique)
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