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We prove that overholonomic complexes over $U$ are stables by direct images, inverse images, extraordinary inverse images, extraordinary direct images, dual functors. Moreover, in the smooth case, we check that unit-root overconvergent $F$-isocrystals are overholonomic. 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We prove that overholonomic complexes over $U$ are stables by direct images, inverse images, extraordinary inverse images, extraordinary direct images, dual functors. Moreover, in the smooth case, we check that unit-root overconvergent $F$-isocrystals are overholonomic. 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