Categories of quantum liquids I

We develop a mathematical theory of separable higher categories based on Gaiotto and Johnson-Freyd's work condensation completion. Based this theory, we prove some fundamental results $E_m$-multi-fusion their centers. also outline unitary $*$-version After these preparations, the idea topological Wick rotation, unified all quantum liquids, which include orders, SPT/SET symmetry-breaking orders CFT-like gapless phases. explain that liquid consists two parts, skeleton local symmetry, show $n$D liquids form $*$-condensation complete category whose equivalence type can be computed explicitly from simple coslice 1-category.