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3
  • $\begingroup$ It would be enough to find an example in sets, categories or groups, cause the latter embeds into simplicial sets (preserving directed colimits and monomorphisms). In sets, unluckily, there are no examples, because the two infinite unions always have the same cardinality. $\endgroup$
    – Andrea Marino
    Commented Jun 22, 2019 at 9:10
  • 5
    $\begingroup$ @Andrea, why don't you write that up? You could take for example $\mathbb{Z} \to \mathbb{Z} \to \ldots$ where in one case it's all identity maps, and in the other it's all multiplication by 2 (in groups). $\endgroup$
    – Todd Trimble ♦
    Commented Jun 22, 2019 at 11:29
  • $\begingroup$ Yeah, sure! I thought about that in ordinals with multiplication by 2 in omega, but didn't realize we could do it in groups more easily (in ordinals, honestly, I wouldnt know how to show it)! $\endgroup$
    – Andrea Marino
    Commented Jun 23, 2019 at 0:19