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How about just covering a type by a 0-type?
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One option would be the solution to the coherence problem for Categories with Families (CWFs). Define a wild CWF as a CWF-algebra with no truncation. The question is whether the usual set-truncated initial CWF is weakly initial for wild CWFs. By initial I mean given a set of generating types and terms (otherwise everything is empty). We don’t yet have a construction for this even using 2LTT but we think it should be possible using semi-simplicial types. On the other hand we should be able to encode semi-simplicial types in the initial CWF (ok we may need some Pi-types) and hence the solution to the coherence pro0blem would imply the constructability of semi-simplicial types.
Thorsten
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