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 Jan26 awarded Popular Question Jul2 awarded Curious Feb18 accepted How does expanding by Taylor's theorem work here? Feb18 comment How does expanding by Taylor's theorem work here? Thank you! And wolfram has a similar explanation of this (Eq. 27). Feb14 comment How does expanding by Taylor's theorem work here? Thank you, it's very helpful to know what the equivalent modern terminology is! One more silly question though, how does the Taylor theorem fit into here? I.e. what is it's purpose? Feb13 accepted What does Universal mapping property for a free monoid mean? Feb13 asked How does expanding by Taylor's theorem work here? Nov18 accepted Isn't every Endofunctor an identity Functor? Nov16 comment Isn't every Endofunctor an identity Functor? @Brad I think I understand what you mean! (I think you should put it in an answer.) I am just finding it hard to keep track of where the category is used as a concrete entity (i.e. defined exactly by it's set of objects, morphisms etc) and where it is used as a "domain" or "range" for things (I guess that would only be in functors). Nov16 comment Isn't every Endofunctor an identity Functor? @Brad Thanks, yes I meant $1$, fixed! Nov16 revised Isn't every Endofunctor an identity Functor? edited body Nov15 revised Isn't every Endofunctor an identity Functor? added 576 characters in body Nov15 comment What's the difference between an endofunctor and a morphism? Great answer. But that describes the difference between morphisms and functors. Do you mind helping me distinguish between functors and endofunctors? Nov15 comment Isn't every Endofunctor an identity Functor? So... you are saying simple reordering of objects... and then changing all morphisms to point to correct objects again. Wouldn't that still be an identity (kind of)? I mean what's the difference between ordering and a successor - aren't they the same? Nov15 comment Isn't every Endofunctor an identity Functor? @camccann Perhaps I don't know what $X\mapsto \{0,1\}\times X$ means... could you explain? Nov15 comment Isn't every Endofunctor an identity Functor? But... that changes the set of objects in the category, wouldn't that change the category $A$ to something like $A'$? Nov15 comment Isn't every Endofunctor an identity Functor? But doesn't that change the set of "objects"? Now we only have one object! I thought category $A$ is only equal to another category $A$ if all objects and morphisms are the same? Nov15 asked Isn't every Endofunctor an identity Functor? Nov13 awarded Quorum Nov13 accepted Why is free monoid called Free?