  We give a variant of Artin algebraization along closed subschemes and closed
substacks. Our main application is the existence of \'etale, smooth, or
syntomic neighborhoods of closed subschemes and closed substacks. In
particular, we prove local structure theorems for stacks and their derived
counterparts and the existence of henselizations along linearly fundamental
closed substacks. These results establish the existence of Ferrand pushouts,
which answers positively a question of Temkin-Tyomkin.
