Apparently the QM and condensed matter people use the term "defect" for a (possibly non-invertible) transformation (semigroup or similar), and a "symmetry" is a

Apparently the QM and condensed matter people use the term "defect" for a (possibly non-invertible) transformation (semigroup or similar), and a "symmetry" is an "invertible" "defect". https://physics.stackexchange.com/questions/561118/why-should-symmetries-be-described-by-invertible-transformations https://physics.stackexchange.com/questions/561118/why-shoul...