{"action":"created","comment":{"url":"https://api.github.com/repos/UniMath/UniMath/pulls/comments/67618311","id":67618311,"diff_hunk":"@@ -0,0 +1,103 @@\n+(** A direct definition of finite coproducts by using arbitrary coproducts *)\n+\n+Require Import UniMath.Foundations.Basics.PartD.\n+Require Import UniMath.Foundations.Basics.Propositions.\n+Require Import UniMath.Foundations.Basics.Sets.\n+\n+Require Import UniMath.Foundations.Combinatorics.StandardFiniteSets.\n+\n+Require Import UniMath.CategoryTheory.total2_paths.\n+Require Import UniMath.CategoryTheory.precategories.\n+Require Import UniMath.CategoryTheory.UnicodeNotations.\n+Require Import UniMath.CategoryTheory.ProductPrecategory.\n+Require Import UniMath.CategoryTheory.limits.arbitrary_coproducts.\n+Require Import UniMath.CategoryTheory.limits.coproducts.\n+Require Import UniMath.CategoryTheory.limits.initial.\n+\n+(** Definition of finite coproduct. *)\n+Section finite_coproduct_def.\n+\n+  Variable C : precategory.\n+\n+  Definition FinCoproducts :=\n+    forall (n : nat) (a : stn n -> C), ArbitraryCoproductCocone (stn n) C a.\n+  Definition hasFinCoproducts := ishinh FinCoproducts.\n+\n+End finite_coproduct_def.\n+\n+(** In the following section we prove that initial object and coproducts imply\n+  finite coproducts. *)\n+Section finite_coproduct_criteria.\n+  Variable C : precategory.\n+  Hypothesis hs : has_homsets C.\n+\n+  (* Couldn't find the following elsewhere. *)\n+  Definition unit_to_ob (c : C) : unit -> C := fun tt : unit => c.","path":"UniMath/CategoryTheory/limits/finite_coproducts.v","position":35,"original_position":35,"commit_id":"85a531307055a85984e3ec16737ef5c805d06780","original_commit_id":"85a531307055a85984e3ec16737ef5c805d06780","user":{"login":"benediktahrens","id":1106102,"avatar_url":"https://avatars.githubusercontent.com/u/1106102?v=3","gravatar_id":"","url":"https://api.github.com/users/benediktahrens","html_url":"https://github.com/benediktahrens","followers_url":"https://api.github.com/users/benediktahrens/followers","following_url":"https://api.github.com/users/benediktahrens/following{/other_user}","gists_url":"https://api.github.com/users/benediktahrens/gists{/gist_id}","starred_url":"https://api.github.com/users/benediktahrens/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/benediktahrens/subscriptions","organizations_url":"https://api.github.com/users/benediktahrens/orgs","repos_url":"https://api.github.com/users/benediktahrens/repos","events_url":"https://api.github.com/users/benediktahrens/events{/privacy}","received_events_url":"https://api.github.com/users/benediktahrens/received_events","type":"User","site_admin":false},"body":"This is `termfun` in Foundations.Basics.PartA.","created_at":"2016-06-19T14:59:10Z","updated_at":"2016-06-19T14:59:10Z","html_url":"https://github.com/UniMath/UniMath/pull/364#discussion_r67618311","pull_request_url":"https://api.github.com/repos/UniMath/UniMath/pulls/364","_links":{"self":{"href":"https://api.github.com/repos/UniMath/UniMath/pulls/comments/67618311"},"html":{"href":"https://github.com/UniMath/UniMath/pull/364#discussion_r67618311"},"pull_request":{"href":"https://api.github.com/repos/UniMath/UniMath/pulls/364"}}},"pull_request":{"url":"https://api.github.com/repos/UniMath/UniMath/pulls/364","id":74329966,"html_url":"https://github.com/UniMath/UniMath/pull/364","diff_url":"https://github.com/UniMath/UniMath/pull/364.diff","patch_url":"https://github.com/UniMath/UniMath/pull/364.patch","issue_url":"https://api.github.com/repos/UniMath/UniMath/issues/364","number":364,"state":"open","locked":false,"title":"Added some results on arbitrary (co)products","user":{"login":"tpannila","id":3755739,"avatar_url":"https://avatars.githubusercontent.com/u/3755739?v=3","gravatar_id":"","url":"https://api.github.com/users/tpannila","html_url":"https://github.com/tpannila","followers_url":"https://api.github.com/users/tpannila/followers","following_url":"https://api.github.com/users/tpannila/following{/other_user}","gists_url":"https://api.github.com/users/tpannila/gists{/gist_id}","starred_url":"https://api.github.com/users/tpannila/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/tpannila/subscriptions","organizations_url":"https://api.github.com/users/tpannila/orgs","repos_url":"https://api.github.com/users/tpannila/repos","events_url":"https://api.github.com/users/tpannila/events{/privacy}","received_events_url":"https://api.github.com/users/tpannila/received_events","type":"User","site_admin":false},"body":"Hi Benedikt and others.\r\n\r\nI managed to formalize the following results about arbitrary (co)products:\r\n- Construction of an arbitrary (co)product from two arbitrary (co)products and\r\n  the assumption that we have a (co)product of the two arbitrary (co)products.\r\n- Construction of a (co)product from an arbitrary (co)product of two elements\r\n  and vice versa.\r\n  \r\n* In the proofs I have used eapply and Unshelve. Should I try to remove\r\n  these?\r\n* Are there other things I should do to the proofs?\r\n\r\nTo prove these, I needed some general results which should probably be moved\r\ninto some other files.\r\n- The lemmas and definitions with name \"coprod_families*\" are both in the\r\n  files coproduct.v and product.v. Are these kind of definitions and lemmas\r\n  already done somewhere? If not, where one should move these? Should these\r\n  be renamed?\r\n- In product.v and coproduct.c I have the \"tworec\", \"stn2ind\", and\r\n  \"pair_to_stn2*\". Where one should move these? Should these be renamed?\r\n","created_at":"2016-06-18T06:57:53Z","updated_at":"2016-06-19T14:59:10Z","closed_at":null,"merged_at":null,"merge_commit_sha":"95ebd0bdccd8b8b75cd201a96be156a7fe916aad","assignee":null,"milestone":null,"commits_url":"https://api.github.com/repos/UniMath/UniMath/pulls/364/commits","review_comments_url":"https://api.github.com/repos/UniMath/UniMath/pulls/364/comments","review_comment_url":"https://api.github.com/repos/UniMath/UniMath/pulls/comments{/number}","comments_url":"https://api.github.com/repos/UniMath/UniMath/issues/364/comments","statuses_url":"https://api.github.com/repos/UniMath/UniMath/statuses/85a531307055a85984e3ec16737ef5c805d06780","head":{"label":"tpannila:arbprods","ref":"arbprods","sha":"85a531307055a85984e3ec16737ef5c805d06780","user":{"login":"tpannila","id":3755739,"avatar_url":"https://avatars.githubusercontent.com/u/3755739?v=3","gravatar_id":"","url":"https://api.github.com/users/tpannila","html_url":"https://github.com/tpannila","followers_url":"https://api.github.com/users/tpannila/followers","following_url":"https://api.github.com/users/tpannila/following{/other_user}","gists_url":"https://api.github.com/users/tpannila/gists{/gist_id}","starred_url":"https://api.github.com/users/tpannila/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/tpannila/subscriptions","organizations_url":"https://api.github.com/users/tpannila/orgs","repos_url":"https://api.github.com/users/tpannila/repos","events_url":"https://api.github.com/users/tpannila/events{/privacy}","received_events_url":"https://api.github.com/users/tpannila/received_events","type":"User","site_admin":false},"repo":{"id":60917018,"name":"UniMath","full_name":"tpannila/UniMath","owner":{"login":"tpannila","id":3755739,"avatar_url":"https://avatars.githubusercontent.com/u/3755739?v=3","gravatar_id":"","url":"https://api.github.com/users/tpannila","html_url":"https://github.com/tpannila","followers_url":"https://api.github.com/users/tpannila/followers","following_url":"https://api.github.com/users/tpannila/following{/other_user}","gists_url":"https://api.github.com/users/tpannila/gists{/gist_id}","starred_url":"https://api.github.com/users/tpannila/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/tpannila/subscriptions","organizations_url":"https://api.github.com/users/tpannila/orgs","repos_url":"https://api.github.com/users/tpannila/repos","events_url":"https://api.github.com/users/tpannila/events{/privacy}","received_events_url":"https://api.github.com/users/tpannila/received_events","type":"User","site_admin":false},"private":false,"html_url":"https://github.com/tpannila/UniMath","description":"This 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