Demonstrates connections between stratified univalence and Malcev theories in higher algebra, implying new synthetical manipulation methods.
We build a bridge between stratified univalence (a cumulative hierarchy of univalent universes equipped with a transfinite extension step) and the theory of Malcev ∞-theories in higher algebra. The guiding thesis is that stratified univalent foundations provide an internal environment in which Malcev theories, their truncations, and their deformation-theoretic Postnikov data can be expressed and manipulated synthetically.
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Antoni Piotr Kodzis (2026) studied this question.
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