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Oct 19, 2018 at 23:02 comment added M.G. Apologies for the delay! Thank you for editting and clearing up what goes on with both definitions and for including the functorial point of view! I have to admit that after getting used to objects having a $1$ for long time, suddenly removing the unit can be a bit confusing and difficult to track down all the properties one is accustomed to that fail in the non-unital setting.
Oct 19, 2018 at 22:32 vote accept M.G.
Oct 18, 2018 at 12:27 history edited Keith Kearnes CC BY-SA 4.0
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Oct 18, 2018 at 1:23 history edited Keith Kearnes CC BY-SA 4.0
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Oct 17, 2018 at 22:11 history edited Keith Kearnes CC BY-SA 4.0
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Oct 17, 2018 at 21:01 history edited Keith Kearnes CC BY-SA 4.0
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Oct 17, 2018 at 20:55 history answered Keith Kearnes CC BY-SA 4.0