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I'll come by to get you at 8 tomorrow morning.
Literal
Tomorrow [possessive-の] morning 8-o'clock [at-に] inviting [to-に] go.
誘いに行く uses the purpose-marker に: [verb stem]に + motion verb = 'go (to do X).' 誘い is the stem of 誘う ('to invite'), so 誘いに行く = 'go in order to invite.' This pattern is limited to motion verbs (行く, 来る, 帰る) and is extremely common for expressing errands and planned actions.