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Thanks! I changed the name again to weakly initial object, since nLab pages are generally named with nouns, but kept “weakly initial” as a redirect. In general when changing the names of pages it’s useful to keep the old ones as redirects; a redirect is usually added automatically by the software when changing the name (maybe you have to click back in the main text box?) although we usually move all the redirects to the bottom instead of the top.
I also cross-linked with weak colimit.
I have tried to polished-up this entry a little:
Adjusted the wording in the Definition section.
Fixed broken link to weak adjoint.
Added cross-link with strict initial object.
Added floating context menus “Category theory” and “Limits and colimits”.
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