27 lines
947 B
Text
27 lines
947 B
Text
import logic
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inductive category (ob : Type) (mor : ob → ob → Type) : Type :=
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mk : Π (comp : Π⦃A B C : ob⦄, mor B C → mor A B → mor A C)
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(id : Π {A : ob}, mor A A),
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(Π {A B C D : ob} {f : mor A B} {g : mor B C} {h : mor C D},
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comp h (comp g f) = comp (comp h g) f) →
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(Π {A B : ob} {f : mor A B}, comp f id = f) →
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(Π {A B : ob} {f : mor A B}, comp id f = f) →
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category ob mor
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class category
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namespace category
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section sec_cat
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parameter A : Type
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inductive foo :=
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mk : A → foo
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class foo
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parameters {ob : Type} {mor : ob → ob → Type} {Cat : category ob mor}
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abbreviation compose := rec (λ comp id assoc idr idl, comp) Cat
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abbreviation id := rec (λ comp id assoc idr idl, id) Cat
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infixr `∘`:60 := compose
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inductive is_section {A B : ob} (f : mor A B) : Type :=
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mk : ∀g, g ∘ f = id → is_section f
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end sec_cat
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end category
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