{"action":"created","issue":{"url":"https://api.github.com/repos/UniMath/UniMath/issues/917","repository_url":"https://api.github.com/repos/UniMath/UniMath","labels_url":"https://api.github.com/repos/UniMath/UniMath/issues/917/labels{/name}","comments_url":"https://api.github.com/repos/UniMath/UniMath/issues/917/comments","events_url":"https://api.github.com/repos/UniMath/UniMath/issues/917/events","html_url":"https://github.com/UniMath/UniMath/pull/917","id":300076923,"number":917,"title":"Add initial and terminal objects to precategory of types","user":{"login":"siddharthist","id":4294323,"avatar_url":"https://avatars3.githubusercontent.com/u/4294323?v=4","gravatar_id":"","url":"https://api.github.com/users/siddharthist","html_url":"https://github.com/siddharthist","followers_url":"https://api.github.com/users/siddharthist/followers","following_url":"https://api.github.com/users/siddharthist/following{/other_user}","gists_url":"https://api.github.com/users/siddharthist/gists{/gist_id}","starred_url":"https://api.github.com/users/siddharthist/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/siddharthist/subscriptions","organizations_url":"https://api.github.com/users/siddharthist/orgs","repos_url":"https://api.github.com/users/siddharthist/repos","events_url":"https://api.github.com/users/siddharthist/events{/privacy}","received_events_url":"https://api.github.com/users/siddharthist/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":0,"created_at":"2018-02-26T00:23:44Z","updated_at":"2018-02-26T01:12:51Z","closed_at":null,"author_association":"COLLABORATOR","pull_request":{"url":"https://api.github.com/repos/UniMath/UniMath/pulls/917","html_url":"https://github.com/UniMath/UniMath/pull/917","diff_url":"https://github.com/UniMath/UniMath/pull/917.diff","patch_url":"https://github.com/UniMath/UniMath/pull/917.patch"},"body":"I also have what I imagine is a basic question. Does this (pre)category have other (co)limits?\r\n\r\nI was trying to prove the universal property of the coproduct, but didn't really get anywhere:\r\n```coq\r\nLemma coprod_universal :\r\n  ∏ A B C (f g : A ⨿ B → C),\r\n    (f ∘ inl = g ∘ inl × f ∘ inr = g ∘ inr) ≃ f = g.\r\nProof.\r\n  intros ? ? ? f g.\r\n  intermediate_weq (f ~ g).\r\n  - use weq_iso.\r\n    intros pair.\r\n    intro copair; induction copair.\r\n    + apply (toforallpaths _ _ _ (pr1 pair)).\r\n    + apply (toforallpaths _ _ _ (pr2 pair)).\r\n    + intro homot.\r\n      use dirprodpair;\r\n        apply maponpaths;\r\n        apply funextsec;\r\n        assumption.\r\n    + intro pair; cbn.\r\n      admit.\r\n    + intro pair; cbn.\r\n      admit.\r\n  - apply invweq.\r\n    apply weqtoforallpaths.\r\nAdmitted.\r\n```\r\nMaybe this is the problem tackled in https://arxiv.org/pdf/1304.0680v3.pdf ?"},"comment":{"url":"https://api.github.com/repos/UniMath/UniMath/issues/comments/368363811","html_url":"https://github.com/UniMath/UniMath/pull/917#issuecomment-368363811","issue_url":"https://api.github.com/repos/UniMath/UniMath/issues/917","id":368363811,"user":{"login":"DanGrayson","id":700228,"avatar_url":"https://avatars1.githubusercontent.com/u/700228?v=4","gravatar_id":"","url":"https://api.github.com/users/DanGrayson","html_url":"https://github.com/DanGrayson","followers_url":"https://api.github.com/users/DanGrayson/followers","following_url":"https://api.github.com/users/DanGrayson/following{/other_user}","gists_url":"https://api.github.com/users/DanGrayson/gists{/gist_id}","starred_url":"https://api.github.com/users/DanGrayson/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DanGrayson/subscriptions","organizations_url":"https://api.github.com/users/DanGrayson/orgs","repos_url":"https://api.github.com/users/DanGrayson/repos","events_url":"https://api.github.com/users/DanGrayson/events{/privacy}","received_events_url":"https://api.github.com/users/DanGrayson/received_events","type":"User","site_admin":false},"created_at":"2018-02-26T01:12:51Z","updated_at":"2018-02-26T01:12:51Z","author_association":"OWNER","body":"Can you get it from this theorem in PartD?\r\n```\r\nTheorem weqfunfromcoprodtoprod (X Y Z : UU) :\r\n  weq (coprod X Y -> Z) ((X -> Z) × (Y -> Z)).\r\n```"}}
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