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This paper investigates modal type theories by using a new categorical semantics called change-of-base semantics. Change-of-base semantics is novel in that it is based on (possibly infinitely) iterated enrichment and interpretation of modality as hom objects. In our semantics, the relationship between meta and object levels in multi-staged computation exactly corresponds to the relationship between enriching and enriched categories. As a result, we obtain a categorical explanation of situationsarXiv:1804.02809v2 fatcat:kw5onsgl7vd5lezi7i6irb2b5u