nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpq2h0xy3u7mmdy6huzs5tfzs48rgvq0csvsxnahqmcpgz0f5vv0n7qqqz6t6 (nprofile…z6t6) that's just terminology that i've heard. by the (-1)-truncation of type i mean the type
\[
\sum_{T:\text{Type}}\prod_{x,y:T}(x=_{T}y)
\]
set is then the 0-truncation, and so on. referring to type above is a bit weird to me, since i'm used to thinking about a hierarchy of universes, but based on jon's earlier posts it seems like he's imagining \(\mathcal{U}_{i} \hookrightarrow_{\text{el}_{i}} \text{Type}\), or something similar? again, i'm not super well-equipped to understand a lot of what i'm reading here