Today’s Catechism sections discuss the concept of God “in Heaven”. Supporting material comes from St. Augustine’s homily “On the Sermon on the Mount”.

IV. "Who Art in Heaven"

2794 This biblical expression does not mean a place (“space"), but a way of being; it does not mean that God is distant, but majestic. Our Father is not "elsewhere": he transcends everything we can conceive of his holiness. It is precisely because he is thrice holy that he is so close to the humble and contrite heart.

"Our Father who art in heaven" is rightly understood to mean that God is in the hearts of the just, as in his holy temple. At the same time, it means that those who pray should desire the one they invoke to dwell in them.54
"Heaven" could also be those who bear the image of the heavenly world, and in whom God dwells and tarries.55

2795 The symbol of the heavens refers us back to the mystery of the covenant we are living when we pray to our Father. He is in heaven, his dwelling place; the Father's house is our homeland. Sin has exiled us from the land of the covenant,56 but conversion of heart enables us to return to the Father, to heaven.57 Jn Christ, then, heaven and earth are reconciled,58 for the Son alone "descended from heaven" and causes us to ascend there with him, by his Cross, Resurrection, and Ascension.59

2796 When the Church prays "our Father who art in heaven," she is professing that we are the People of God, already seated "with him in the heavenly places in Christ Jesus" and "hidden with Christ in God;"60 yet at the same time, "here indeed we groan, and long to put on our heavenly dwelling."61

[Christians] are in the flesh, but do not live according to the flesh. They spend their lives on earth, but are citizens of heaven.62

IN BRIEF

2802 "Who art in heaven" does not refer to a place but to God's majesty and his presence in the hearts of the just. Heaven, the Father's house, is the true homeland toward which we are heading and to which, already, we belong.

In his homily “On the Sermon on the Mount” (2, 5, 18), St. Augustine discusses the concept of God in Heaven.

18. And for the purpose of showing this, when we stand at prayer, we turn to the east, whence the heaven rises: not as if God also were dwelling there, in the sense that He who is everywhere present, not as occupying space, but by the power of His majesty, had forsaken the other parts of the world; but in order that the mind may be admonished to turn to a more excellent nature, i.e. to God, when its own body, which is earthly, is turned to a more excellent body, i.e. to a heavenly one. It is also suitable for the different stages of religion, and expedient in the highest degree, that in the minds of all, both small and great, there should be cherished worthy conceptions of God. And therefore, as regards those who as yet are taken up with the beauties that are seen, and cannot think of anything incorporeal, inasmuch as they must necessarily prefer heaven to earth, their opinion is more tolerable, if they believe God, whom as yet they think of after a corporeal fashion, to be in heaven rather than upon earth: so that when at any future time they have learned that the dignity of the soul exceeds even a celestial body, they may seek Him in the soul rather than in a celestial body even; and when they have learned how great a distance there is between the souls of sinners and of the righteous, just as they did not venture, when as yet they were wise only after a carnal fashion, to place Him on earth, but in heaven, so afterwards with better faith or intelligence they may seek Him again in the souls of the righteous rather than in those of sinners. Hence, when it is said, Our Father which art in heaven, it is rightly understood to mean in the hearts of the righteous, as it were in His holy temple. And at the same time, in such a way that he who prays wishes Him whom he invokes to dwell in himself also; and when he strives after this, practises righteousness—a kind of service by which God is attracted to dwell in the soul.

Footnotes

54 St. Augustine, De serm. Dom. in monte 2, 5, 18: PL 34, 1277.
55 St. Cyril of Jerusalem, Catech. myst. 5:11: PG 33, 1117.
56 Cf. ⇒ Gen 3.
57 ⇒ Jer 3:19- ⇒ 4:1a; ⇒ Lk 15:18, ⇒ 21.
58 Cf. ⇒ Isa 45:8; ⇒ Ps 85:12.
59 ⇒ Jn 3:13; ⇒ 12:32; ⇒ 14 2-3; ⇒ 16:28; ⇒ 20:17; ⇒ Eph 4:9-10; ⇒ Heb 1:3; ⇒ 2:13.
60 ⇒ Eph 2:6; ⇒ Col 3:3.
61 ⇒ 2 Cor 5:2; cf. ⇒ Phil 3:20; ⇒ Heb 13:14.
62 Ad Diognetum 5: PG 2, 1173.