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No.

Agile is a subset of TPS (toyota production system)/Lean applied to software.

Actually, lean is lean applied to software. Agile is Henry Ford's interpretation of lean applied to his factories, applied to software.

And scrum? TPS is explicitly an influence on scrum.

Scrum is just an instance of the agile manifesto. TPS/Lean > Agile > Scrum.

Kanban for example is another instance of the agile manifesto.

Scrum existed before the agile manifesto. It's probability more accurate to say Agile is a mix of those things.