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Use glueTrianglesʳ in definition of _∘_ for slice categories #491

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Merged
JacquesCarette merged 1 commit into from
Nov 16, 2025
Merged

Use glueTrianglesʳ in definition of _∘_ for slice categories #491

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8 changes: 1 addition & 7 deletions src/Categories/Category/Slice.agda
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Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,6 @@ open HomReasoning
open Equiv

open import Level
open import Function.Base using (_$_)
open import Relation.Binary.Core using (Rel)

open import Categories.Morphism.Reasoning 𝒞
Expand Down Expand Up @@ -42,7 +41,7 @@ Slice A = record
; _≈_ = λ where
(slicearr {f} _) (slicearr {g} _) → f ≈ g
; id = slicearr identityʳ
; _∘_ = _∘′_
; _∘_ = λ (slicearr △) (slicearr △′) → slicearr (glueTrianglesʳ △ △′)
; assoc = assoc
; sym-assoc = sym-assoc
; identityˡ = identityˡ
Expand All @@ -55,8 +54,3 @@ Slice A = record
}
; ∘-resp-≈ = ∘-resp-≈
}
where _∘′_ : Slice⇒ Y Z → Slice⇒ X Y → Slice⇒ X Z
_∘′_ {Y = sliceobj y} {Z = sliceobj z} {X = sliceobj x} (slicearr {g} △) (slicearr {f} △′) = slicearr $ begin
z ∘ g ∘ f ≈⟨ pullˡ △ ⟩
y ∘ f ≈⟨ △′ ⟩
x ∎