We investigate pure monomorphisms and pure epimorphisms in varieties of universal algebras with applications to equationally compact (= pure injective) algebras, pure projective algebras and perfect varieties.
Borceux, F., & Rosicky, J. (2007). Purity in algebra. Algebra Universalis, 56(1), 17-35. https://doi.org/10.1007/s00012-006-1977-x (Original work published 2007)