Front-door adjustment identifies an exposure effect through an observed mediator when the mediator intercepts every directed exposure-outcome path, the exposure-mediator relation has no unblocked backdoor path, and exposure blocks every backdoor path from mediator to outcome.
Conditional front-door adjustment applies the front-door argument within strata of observed covariates and then averages over those covariates. The covariates must remove exposure-mediator confounding, while the exposure together with the covariates must remove mediator-outcome confounding.

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