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While I didn’t write this:
The point is that morphisms are regarded as stand-ins for (the families of) their fibers: In saying that such a morphism “is -small” one means to say that all its fibers are -small, hence that it represents a family of -small sets.
Here the index-set of these -small sets itself need not be -small. In this sense every identity morphism counts as being -small, since it represents a family of singleton sets.
Finally, the notation “” is meant to refer to the “elements” of the universe, I think.
(All of this would be good to further clarify in the entry. But I won’t edit at the moment.)
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