Capitalization of "neo-scholasticism" [duplicate]
Academic writing is usually in compliance with the relevant institution or publisher's style guide. As you see here, they differ sometimes:
Penn State University
Capitalize names of cultural movements and styles if they are derived from proper nouns; otherwise they should be lowercased: Cynicism, Doric, Gothic, Neoplatonism, Pre-Raphaelite, Romanesque; but baroque, classical, cubism, Dadaism, modernism, neoclassicism, postmodernism, romanticism.
Capitalization (Penn State)
However...
Association of Art Editors:
In general, sharply delimited period titles are capitalized, whereas broad periods and terms applicable to several periods are not:
Archaic period Baroque Early Renaissance High Renaissance Early Christian Gothic Greek Classicism of the fifth century (otherwise, classicism) Imperial Impressionism Islamic Mannerist Middle Ages Neoclassicism (for the late-18th-century movement; otherwise, neoclassicism) Post-Impressionism Pre-Columbian, Precolumbian Rococo Roman Romanesque Romantic period antique, antiquity classicism (see above) medieval modern, modernism neoclassicism (see above) postmodern prehistoric quattrocento
Association of Art Editors Style Guide
Some sources advise neo-Scholasticism and Merriam Webster has neo-scholasticism.