diff --git a/proposal/macros.tex b/proposal/macros.tex index 604ae8b..aec0c67 100644 --- a/proposal/macros.tex +++ b/proposal/macros.tex @@ -5,6 +5,7 @@ \newcommand{\defeq}{\coloneqq} \newcommand{\bN}{\mathbb{N}} \newcommand{\bC}{\mathbb{C}} +\newcommand{\bX}{\mathbb{X}} \newcommand{\to}{\rightarrow}} \newcommand{\mto}{\mapsto}} \newcommand{\UU}{\ensuremath{\mathcal{U}}\xspace} diff --git a/src/Cat/Functor.agda b/src/Cat/Functor.agda index 5965f72..c0bebc1 100644 --- a/src/Cat/Functor.agda +++ b/src/Cat/Functor.agda @@ -8,18 +8,16 @@ open import Cat.Category record Functor {ℓc ℓc' ℓd ℓd'} (C : Category ℓc ℓc') (D : Category ℓd ℓd') : Set (ℓc ⊔ ℓc' ⊔ ℓd ⊔ ℓd') where - private - open module C = Category C - open module D = Category D + open Category field - func* : C.Object → D.Object - func→ : {dom cod : C.Object} → C.Arrow dom cod → D.Arrow (func* dom) (func* cod) - ident : { c : C.Object } → func→ (C.𝟙 {c}) ≡ D.𝟙 {func* c} + func* : C .Object → D .Object + func→ : {dom cod : C .Object} → C .Arrow dom cod → D .Arrow (func* dom) (func* cod) + ident : { c : C .Object } → func→ (C .𝟙 {c}) ≡ D .𝟙 {func* c} -- TODO: Avoid use of ugly explicit arguments somehow. -- This guy managed to do it: -- https://github.com/copumpkin/categories/blob/master/Categories/Functor/Core.agda - distrib : { c c' c'' : C.Object} {a : C.Arrow c c'} {a' : C.Arrow c' c''} - → func→ (a' C.⊕ a) ≡ func→ a' D.⊕ func→ a + distrib : { c c' c'' : C .Object} {a : C .Arrow c c'} {a' : C .Arrow c' c''} + → func→ (C ._⊕_ a' a) ≡ D ._⊕_ (func→ a') (func→ a) module _ {ℓ ℓ' : Level} {A B C : Category ℓ ℓ'} (F : Functor B C) (G : Functor A B) where open Functor