Church going up, built right inside school (5,4)

I believe the answer is:

notre dame

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'church' is the definition.
(I've seen this before)

I don't understand how the remainder of the clue works.

(Other definitions for notre dame that I've seen before include "Great cathedral of Paris" , "High Church" , "Parisian landmark" , "Victor Hugo wrote 'The Hunchback of . . . . . . . . .'" , "...in another [CATHEDRAL]" .)

I've seen this clue in The Independent.

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