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Oct 25, 2021 at 22:25 vote accept varkor
Oct 25, 2021 at 22:25 comment added varkor Ah, of course! Thank you, I am satisfied this answers my question. Sorry for the delay.
Oct 25, 2021 at 14:44 comment added Paul Taylor I wrote out the definition of when $A$ is free on $X$, ie $A\cong F X$, and said that every $A$ is free on something.
Oct 25, 2021 at 14:40 comment added varkor Could you spell out a little more why this property is the same as essential surjectivity? (In particular, I do not want to assume equalisers.) I'm happy to assume $F$ is bijective-on-objects or even identity-on-objects if that makes things simpler.
Oct 4, 2021 at 18:17 comment added varkor Thanks, I shall digest this and get back to you.
Oct 3, 2021 at 20:15 history edited Paul Taylor CC BY-SA 4.0
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Oct 3, 2021 at 17:06 history answered Paul Taylor CC BY-SA 4.0