Mercurial > hg > Members > kono > Proof > category

comparison CCChom.agda @ 808:e4cc2ccd0f06

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
...
author Shinji KONO <kono@ie.u-ryukyu.ac.jp>
date Fri, 26 Apr 2019 19:50:27 +0900
parents 91a2efb67462
children 0976d576f5f6
comparison
equal deleted inserted replaced
807:91a2efb67462 808:e4cc2ccd0f06
635 fmap : {G : SM} { a b : Obj (DX G) } → Hom (DX G) a b → fobj {G} a → fobj {G} b 635 fmap : {G : SM} { a b : Obj (DX G) } → Hom (DX G) a b → fobj {G} a → fobj {G} b
636 fmap {G} {a} {a} (id a) = λ z → z 636 fmap {G} {a} {a} (id a) = λ z → z
637 fmap {G} {a} {(atom b)} (next {a} {c} (arrow x) f) = λ z → smap G x ( k z ) where 637 fmap {G} {a} {(atom b)} (next {a} {c} (arrow x) f) = λ z → smap G x ( k z ) where
638 k : fobj a → fobj {G} c 638 k : fobj a → fobj {G} c
639 k z = fmap f z 639 k z = fmap f z
640 fmap {G} {a} {b} (next (id b) f) = fmap f 640 fmap {G} {a} {b} (next (id b) f) = λ z → k z where
641 k : fobj a → fobj {G} b
642 k z = fmap f z
641 fmap {G} {a} {⊤} (next (○ b) f) = λ _ → OneObj' 643 fmap {G} {a} {⊤} (next (○ b) f) = λ _ → OneObj'
642 fmap {G} {a} {b} (next {a} {x ∧ y} {b} π f) = λ z → proj₁ ( k z ) where 644 fmap {G} {a} {b} (next {a} {x ∧ y} {b} π f) = λ z → proj₁ ( k z ) where
643 k : fobj a → fobj x /\ fobj y 645 k : fobj a → fobj x /\ fobj y
644 k z = fmap f z 646 k z = fmap f z
645 fmap {G} {a} {b} (next {.a} {x ∧ y} π' f) = λ z → proj₂ ( k z ) where 647 fmap {G} {a} {b} (next {.a} {x ∧ y} π' f) = λ z → proj₂ ( k z ) where
646 k : fobj a → fobj x /\ fobj y 648 k : fobj a → fobj x /\ fobj y
647 k z = fmap f z 649 k z = fmap f z
648 fmap {G} {a} {b} (next {.a} {(x <= y) ∧ y} {.b} ε f) = λ z → ( proj₁ (k z))( proj₂ (k z)) where 650 fmap {G} {a} {b} (next {.a} {(x <= y) ∧ y} {.b} ε f) = λ z → ( proj₁ (k z))( proj₂ (k z)) where
649 k : fobj a → (fobj y → fobj x) /\ fobj y 651 k : fobj a → (fobj y → fobj x) /\ fobj y
650 k z = fmap f z 652 k z = fmap f z
651 fmap {G} {a} {b} (next {.a} {c} (_・_ {c} {d} {b} f g) h) = λ z → fmap ( next f (id d)) ( fmap (next g (id c )) ( fmap h z )) 653 fmap {G} {a} {b} (next (f ・ g ) h) = {!!} -- λ z → fmap (next f (next g h )) z
652 fmap {G} {a} {(_ ∧ _)} (next < f , g > h) = λ z → ( fmap (next f h) z , fmap (next g h) z) 654 fmap {G} {a} {(_ ∧ _)} (next < f , g > h) = λ z → ( fmap (next f h) z , fmap (next g h) z)
653 fmap {G} {a} {(c <= b)} (next {_} {d} (f *) g ) = λ x y → fmap (next f (id (d ∧ b))) ( fmap g x , y ) 655 fmap {G} {a} {(c <= b)} (next {_} {d} (f *) g ) = {!!} -- λ x y → fmap (next f (id (d ∧ b))) ( fmap g x , y )
654 656
655 CS : {G : SM } → Functor (DX G) (Sets {Level.zero}) 657 CS : {G : SM } → Functor (DX G) (Sets {Level.zero})
656 FObj CS a = fobj a 658 FObj CS a = fobj a
657 FMap (CS {G}) {a} {b} f = fmap {G} {a} {b} f 659 FMap (CS {G}) {a} {b} f = fmap {G} {a} {b} f
658 isFunctor (CS {G}) = isf where 660 isFunctor (CS {G}) = isf where