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Use glueTrianglesʳ in definition of _∘_ for slice categories
It has a comment saying it's basically composition in the over category, so it might as well be composition in the over category
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src/Categories/Category/Slice.agda

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@@ -10,7 +10,6 @@ open HomReasoning
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open Equiv
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open import Level
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open import Function.Base using (_$_)
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open import Relation.Binary.Core using (Rel)
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open import Categories.Morphism.Reasoning 𝒞
@@ -42,7 +41,7 @@ Slice A = record
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; _≈_ = λ where
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(slicearr {f} _) (slicearr {g} _) f ≈ g
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; id = slicearr identityʳ
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; _∘_ = _∘′_
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; _∘_ = λ (slicearr △) (slicearr △′) slicearr (glueTrianglesʳ △ △′)
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; assoc = assoc
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; sym-assoc = sym-assoc
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; identityˡ = identityˡ
@@ -55,8 +54,3 @@ Slice A = record
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}
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; ∘-resp-≈ = ∘-resp-≈
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}
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where _∘′_ : Slice⇒ Y Z Slice⇒ X Y Slice⇒ X Z
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_∘′_ {Y = sliceobj y} {Z = sliceobj z} {X = sliceobj x} (slicearr {g} △) (slicearr {f} △′) = slicearr $ begin
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z ∘ g ∘ f ≈⟨ pullˡ △ ⟩
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y ∘ f ≈⟨ △′ ⟩
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x ∎

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