In a recent answer to a recent question, BCnrd wrote

[...] beyond the coherent case one cannot expect information about a fiber (e.g., vanishing, 6 generators, etc.) to "propogate" to information in a neighborhoood (which would be the spirit behind the choice of word "coherent", I suppose). [...]

Is that what motivates the adjective coherent? Is this documented somewhere?

In a recent answer to a recent question, BCnrd wrote

[...] beyond the coherent case one cannot expect information about a fiber (e.g., vanishing, 6 generators, etc.) to "propogate" to information in a neighborhoood (which would be the spirit behind the choice of word "coherent", I suppose). [...]

Is that what motivates the adjective coherent? Is this documented somewhere?