On elementary (infinity,1)-toposes:
Nima Rasekh, A Theory of Elementary Higher Toposes, (arXiv:1805.03805)
Nima Rasekh, Yoneda Lemma for Elementary Higher Toposes, (arXiv:1809.01736)
Specifically on natural number objects:
Specifically on n-truncation:
Discussion of straightening and unstraightening for (∞,n)-categories:
On fractured -toposes in condensed mathematics (cf. condensed local contractibility):
On the twisted arrow construction in (infinity,1)-category theory:
For the concept of a universal shadow of a bicategory and an extension of shadows to (∞,2)-categories, see
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