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Am I right in understanding that an “amnestic isofibration” is the same as what is sometimes called a “discrete isofibration”, e.g. in this paper?
That seems right. But I’ve never encountered this usage of “discrete isofibration” before, and it seems poorly chosen to me; I would expect a “discrete isofibration” to mean an isofibration with discrete fibers.
Mention conservative functors as a related concept.
I notice the definition of amnestic isofibration is reminiscent of an adjunction. I wonder whether it can be reformulated that way.
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