Definition fld_precategory_data : precategory_data := make_precategory_data fld_precategory_ob_mor (λ (X : fld), (rigisotorigfun (idrigiso X))) (fun (X Y Z : fld) (f : ringfun X Y) (g : ringfun Y Z) => rigfuncomp f g). Local Lemma fld_id_left (X Y : fld) (f : ringfun X Y) : rigfuncomp (rigisotorigfun (idrigiso X)) f = f. Proof. use rigfun_paths. apply idpath. Defined.
Require Import UniMath.Foundations.PartD. Require Import UniMath.Foundations.Propositions. Require Import UniMath.Foundations.Sets. Require Import UniMath.Foundations.UnivalenceAxiom. Require Import UniMath.Algebra.BinaryOperations. Require Import UniMath.Algebra.Monoids. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.CategoryTheory.Core.Categories. Require Import UniMath.CategoryTheory.Core.Isos. Require Import UniMath.CategoryTheory.Core.Univalence.