From 896dc3d29684bdecd906330a62d250ccbeb18f6a Mon Sep 17 00:00:00 2001 From: Leon Vatthauer Date: Wed, 14 Feb 2024 12:03:47 +0100 Subject: [PATCH] update index --- agda/src/index.lagda.md | 11 +++++++++-- 1 file changed, 9 insertions(+), 2 deletions(-) diff --git a/agda/src/index.lagda.md b/agda/src/index.lagda.md index 519eef8..8aab6ea 100644 --- a/agda/src/index.lagda.md +++ b/agda/src/index.lagda.md @@ -57,6 +57,13 @@ Afterwards we also introduce categories of iteration algebras with iteration pre open import Category.Construction.ElgotAlgebras ``` +we can form products and exponentials in a canonical way: + +```agda +open import Category.Construction.ElgotAlgebras.Products +open import Category.Construction.ElgotAlgebras.Exponentials +``` + Free Elgot algebras are free objects in the category of Elgot algebras, we will be needing a notion of stability for them: ```agda @@ -67,7 +74,7 @@ open import Algebra.Elgot.Stable In a CCC stability follows directly ```agda open import Algebra.Elgot.Properties -``` +``` With this in hand we can now define *KX* as a *free Elgot algebra* and proof that under *stability* it is a strong monad. @@ -83,7 +90,7 @@ open import Monad.Instance.K.Commutative open import Monad.Instance.K.EquationalLifting ``` -and lastly we formalize the notion of *pre-Elgot monad* and show that **K** is the initial (strong) pre-Elgot monad. +and lastly we formalize the notion of *(strong) pre-Elgot monad* and show that **K** is the initial (strong) pre-Elgot monad. ```agda open import Monad.PreElgot