A functor $F:\mathcal A\to\mathcal B$ is by definition amnestic if any isomorphism in $\mathcal A$ that is sent by $F$ to an identity is an identity itself.
I fail to see why the term "amnestic" is used for this labeling.
Can someone make me wiser?
Especially a good understanding of used terms is very helpful for my memory when it concerns mathematical concepts.
Thank you in advance.
Perhaps there is some better reason I'm not aware of, but I've always assumed it was just in reference to "forgetful functors". Most typical forgetful functors are amnestic, and it is a convenient property to require of functors you want to behave like the familiar forgetful functors in certain ways. (And indeed, the only context in which I've ever seen amnestic functors used is in discussing an abstract theory of forgetful functors and similar concepts.)