Cyril of Alexandria lays out a coherent Christological-Eucharistic position in his Third Letter to Nestorius : “We proclaim the fleshly death of God’s Only-Begotten Son, Jesus Christ, we confess His return to life from the dead and His ascension into heaven when we perform in church the unbloody service, when we approach the sacramental gifts and are hallowed participants in the holy flesh and precious blood of Christ, Saviour of us all, by receiving not mere flesh (God forbid!) or flesh of a man hallowed by connection with the Word in some unity of dignity or possessing some divine indwelling, but the personal, truly vitalizing flesh of God the Word himself. As God He is by nature Life and because He has become one with His own flesh He declared it vitalizing; and so, though he tells us ‘verily I say unto you, unless you eat the flesh of the Son of Man and drink his blood,’ we must not suppose that it belongs to one of us men (how could man’s flesh be vitalizing by its own nature?) but that it was made the personal possession of Him who for us has become and was called ‘the Son of Man.’”
Ezra Gebremedhin ( Life-giving Blessing: Inquiry into the Eucharistic Doctrine of Cyril of Alexandria ), who quotes this passage notes the implicit contrast between an understanding of the incarnation as union to the “Antiochene” view that the incarnation is primarily an indwelling (34).
Cyril certainly draws this contrast, but I wonder if it’s a felicitous one. Perhaps the divide can be bridged: A strong understanding of divine indwelling (“tabernacling,” John 1:14) might be understood not as an alternative to “union” but as a description of the kind of union the incarnation is. This seems to be the aim of early writers who introduced the notion of “perichoresis” into Christology to express the intimate union of the two natures that remained distinct.
Cyril’s summary statement also ignores the pneumatological dimension of the Eucharist. Christ’s flesh is made vitalizing by His “return to life from the dead and His ascension into heaven,” but Cyril makes no reference to the corresponding gift of the Spirit. There also seems to be some confusion of resurrection and incarnation: At the beginning of the quotation, the vitalizing character of Christ’s flesh seems to be contingent on His death and resurrection, but toward the middle of the quotation Cyril seems to backtrack, rooting the vitality of the flesh in the fact that it has a “connection with the Word” and the fact that the Word made it His own.