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What is the precise definition of "a set's worth" of something, when used in reference to the quantity of something? Does it mean there is a bijective correspondence to the elements of some well-defined set (or perhaps a subset of such set)?

For example, in "Category Theory in Context" Emily Riehl on page 6 gives the following definition: A category is small if it has only a set's worth of arrows.

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    $\begingroup$ I haven't seen it phrased that way very often. It's clear that her intent is that you don't have a proper class of arrows. $\endgroup$
    – Derek Elkins left SE
    Jun 12, 2017 at 23:04
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    $\begingroup$ I agree with Derek Elkins, but I would add that the replacement schema of set theory is important in seeing why this kind of wording makes sense, intuitively. See en.wikipedia.org/wiki/Axiom_schema_of_replacement $\endgroup$
    – user49640
    Jun 13, 2017 at 1:09

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