fact stringlengths 4 3.31k | type stringclasses 14
values | library stringclasses 23
values | imports listlengths 1 59 | filename stringlengths 20 105 | symbolic_name stringlengths 1 89 | docstring stringlengths 0 1.75k ⌀ |
|---|---|---|---|---|---|---|
ptd_from_alg_functor: functor (category_FunctorAlg Id_H) Ptd :=
tpair _ _ is_functor_ptd_from_alg_functor_data. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | ptd_from_alg_functor | null |
isbracketMor {T T' : hss} (β : algebra_mor _ T T') : UU :=
∏ (Z : Ptd) (f : U Z --> `T),
⦃f⦄_{Z} · β = β •• U Z · ⦃f · #U (# ptd_from_alg_functor β)⦄_{Z}. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | isbracketMor | null |
isaprop_isbracketMor (T T' : hss) (β : algebra_mor _ T T') : isaprop (isbracketMor β). | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | isaprop_isbracketMor | null |
ishssMor {T T' : hss} (β : algebra_mor _ T T') : UU
:= isbracketMor β. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | ishssMor | A morphism of hss is a pointed morphism that is compatible with both
[τ] and [fbracket] |
hssMor (T T' : hss) : UU
:= ∑ β : algebra_mor _ T T', ishssMor β. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hssMor | null |
isAlgMor_hssMor {T T' : hss} (β : hssMor T T')
: isAlgMor β := pr1 (pr2 β). | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | isAlgMor_hssMor | null |
isbracketMor_hssMor {T T' : hss} (β : hssMor T T')
: isbracketMor β := pr2 β. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | isbracketMor_hssMor | A morphism of hss is a pointed morphism that is compatible with both
[τ] and [fbracket] |
hssMor_eq1 : β = β' ≃ (pr1 β = pr1 β'). | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hssMor_eq1 | null |
hssMor_eq : β = β' ≃ (β : EndC ⟦ _ , _ ⟧) = β'. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hssMor_eq | null |
isaset_hssMor (T T' : hss) : isaset (hssMor T T'). | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | isaset_hssMor | null |
ishssMor_id (T : hss) : ishssMor (identity (C:=category_FunctorAlg _) (pr1 T)). | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | ishssMor_id | *** Identity morphism of hss |
hssMor_id (T : hss) : hssMor _ _ := tpair _ _ (ishssMor_id T). | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hssMor_id | null |
ishssMor_comp {T T' T'' : hss} (β : hssMor T T') (γ : hssMor T' T'')
: ishssMor (compose (C:=category_FunctorAlg _) (pr1 β) (pr1 γ)). | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | ishssMor_comp | *** Composition of morphisms of hss |
hssMor_comp {T T' T'' : hss} (β : hssMor T T') (γ : hssMor T' T'')
: hssMor T T'' := tpair _ _ (ishssMor_comp β γ). | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hssMor_comp | null |
hss_obmor : precategory_ob_mor. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hss_obmor | null |
hss_precategory_data : precategory_data. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hss_precategory_data | null |
is_precategory_hss : is_precategory hss_precategory_data. | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | is_precategory_hss | null |
hss_precategory : precategory := tpair _ _ is_precategory_hss. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hss_precategory | null |
has_homsets_precategory_hss : has_homsets hss_precategory. | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | has_homsets_precategory_hss | null |
hss_category : category := hss_precategory ,, has_homsets_precategory_hss. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | hss_category | null |
τ := tau_from_alg. | Notation | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | τ | null |
η := eta_from_alg. | Notation | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath"
] | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems.v | η | null |
GenMendlerIteration :
∏ (C : category) (F : functor C C)
(μF_Initial : Initial (FunctorAlg F)) (C' : category)
(X : C') (L : functor C C'),
is_left_adjoint L
→ ∏ ψ : ψ_source C C' X L ⟹ ψ_target C F C' X L,
∃! h : C' ⟦ L ` (InitialObject μF_Initial), X ⟧,
# L (alg_map F (InitialObject μF_Initia... | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | GenMendlerIteration | Lemma 8 |
fusion_law
: ∏ (C : category)
(F : functor C C)
(μF_Initial : Initial (category_FunctorAlg F))
(C' : category)
(X X' : C') (L : functor C C')
(is_left_adj_L : is_left_adjoint L)
(ψ : ψ_source C C' X L ⟹ ψ_target C F C' X L)
(L' : functor C C')
(is_left_adj_L'... | Theorem | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | fusion_law | Lemma 9 |
fbracket_natural
: ∏ (C : category) (CP : BinCoproducts C)
(H : Presignature C C C) (T : hss CP H) (Z Z' : category_Ptd C)
(f : category_Ptd C ⟦ Z, Z' ⟧)
(g : [C,C] ⟦ U Z', `T ⟧),
(`T ∘ # U f : [C, C] ⟦ `T • U Z , `T • U Z' ⟧) · ⦃g⦄_{Z'} = ⦃#U f · g⦄_{Z} . | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | fbracket_natural | Lemma 15 |
compute_fbracket
: ∏ (C : category) (CP : BinCoproducts C)
(H : Presignature C C C) (T : hss CP H) (Z : category_Ptd C)
(f : category_Ptd C ⟦ Z, ptd_from_alg T ⟧),
⦃#U f⦄_{Z} = (`T ∘ # U f : [C, C] ⟦ `T • U Z , `T • U _ ⟧) · ⦃ identity (U (ptd_from_alg T)) ⦄_{ptd_from_alg T}. | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | compute_fbracket | null |
Monad_from_hss
: ∏ (C : category) (CP : BinCoproducts C)
(H : Signature C C C), hss CP H → Monad C. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | Monad_from_hss | Theorem 24 |
hss_to_monad_functor
: ∏ (C : category) (CP : BinCoproducts C)
(H : Signature C C C),
functor (hss_precategory CP H) (category_Monad C). | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | hss_to_monad_functor | Theorem 25 |
faithful_hss_to_monad
: ∏ (C : category) (CP : BinCoproducts C)
(H : Signature C C C), faithful (hss_to_monad_functor C CP H). | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | faithful_hss_to_monad | Lemma 26 |
bracket_for_initial_algebra
: ∏ (C : category) (CP : BinCoproducts C),
(∏ Z : category_Ptd C, GlobalRightKanExtensionExists C C (U Z) C)
→ ∏ (H : Presignature C C C)
(IA : Initial (FunctorAlg (Id_H C CP H)))
(Z : category_Ptd C),
[C, C] ⟦ U Z, U (ptd_from_alg (InitAlg C CP ... | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | bracket_for_initial_algebra | Theorem 28 in three steps:
- the operation itself
- its compatibility with variables
- its compatibility with signature-dependent constructions |
bracket_Thm15_ok_η
: ∏ (C : category) (CP : BinCoproducts C)
(KanExt : ∏ Z : category_Ptd C,
GlobalRightKanExtensionExists C C (U Z) C)
(H : Presignature C C C)
(IA : Initial (FunctorAlg (Id_H C CP H)))
(Z : category_Ptd C)
(f : [C,C] ⟦ U Z, U (ptd_from_alg (Init... | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | bracket_Thm15_ok_η | null |
bracket_Thm15_ok_τ
: ∏ (C : category) (CP : BinCoproducts C)
(KanExt : ∏ Z : category_Ptd C, GlobalRightKanExtensionExists C C (U Z) C)
(H : Presignature C C C)
(IA : Initial (FunctorAlg (Id_H C CP H)))
(Z : category_Ptd C)
(f : [C,C] ⟦ U Z, U (ptd_from_alg (InitAlg C CP H IA)) ⟧),
(... | Lemma | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | bracket_Thm15_ok_τ | null |
Initial_HSS :
∏ (C : category) (CP : BinCoproducts C),
(∏ Z : category_Ptd C,
GlobalRightKanExtensionExists C C (U Z) C)
→ ∏ H : Presignature C C C,
Initial (FunctorAlg (Id_H C CP H))
→ Initial (hss_category CP H). | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | Initial_HSS | Theorem 29 |
Sum_of_Signatures
: ∏ (C D D': category),
BinCoproducts D → Signature C D D' → Signature C D D' → Signature C D D'. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | Sum_of_Signatures | Lemma 30 |
App_Sig
: ∏ (C : category), BinProducts C → Signature C C C. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | App_Sig | Definition 31 |
Lam_Sig
: ∏ (C : category),
Terminal C → BinCoproducts C → BinProducts C → Signature C C C. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | Lam_Sig | Definition 32 |
Flat_Sig
: ∏ (C : category), Signature C C C. | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | Flat_Sig | Definition 33 |
Lam_Flatten
: ∏ (C : category) (terminal : Terminal C)
(CC : BinCoproducts C) (CP : BinProducts C),
(∏ Z : category_Ptd C,
GlobalRightKanExtensionExists C C (U Z) C)
→ ∏ Lam_Initial : Initial (FunctorAlg (Id_H C CC (Lam_Sig C terminal CC CP))),
[C, C] ⟦ (Flat_H C) ` (InitialObject Lam_Initia... | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | Lam_Flatten | Definition 36 |
fbracket_for_LamE_algebra_on_Lam
: ∏ (C : category) (terminal : Terminal C)
(CC : BinCoproducts C) (CP : BinProducts C)
(KanExt : ∏ Z : category_Ptd C, GlobalRightKanExtensionExists C C (U Z) C)
(Lam_Initial : Initial (FunctorAlg (Id_H C CC (Lam_Sig C terminal CC CP))))
(Z : category_Ptd C),
... | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | fbracket_for_LamE_algebra_on_Lam | Lemma 37, construction of the bracket |
EVAL
: ∏ (C : category) (terminal : Terminal C)
(CC : BinCoproducts C) (CP : BinProducts C)
(KanExt : ∏ Z : category_Ptd C, GlobalRightKanExtensionExists C C (U Z) C)
(Lam_Initial : Initial
(FunctorAlg
(Id_H C CC
(LamS... | Definition | SubstitutionSystems | [
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"UniMath",
"Uni... | UniMath/SubstitutionSystems/SimplifiedHSS/SubstitutionSystems_Summary.v | EVAL | Morphism from initial hss to construed hss, consequence of Lemma 37 |
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