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I call the Vopěnka's principle: Every subfunctor of an accessible functor is accessible but other formulations (which may lose equivalence in weak contexts?) are also interesting to me. If this is ...

When reasoning about the category of sets, we usually don't have to worry about the internal/external distinction. For example, if $f : X \rightarrow Y$ is a morphism of sets, then $f$ is either ...