We construct an explicit isomorphism between (truncations of) quiver Hecke
algebras and Elias-Williamson's diagrammatic endomorphism algebras of
Bott-Samelson bimodules. As a corollary, we deduce that the decomposition
numbers of these algebras (including as examples the symmetric groups and
generalised blob algebras) are tautologically equal to the associated
p-Kazhdan-Lusztig polynomials, provided that the characteristic is greater
than the Coxeter number. We hence give an elementary and more explicit proof of
the main theorem of Riche-Williamson's recent monograph and extend their
categorical equivalence to cyclotomic Hecke algebras, thus solving
Libedinsky-Plaza's categorical blob conjecture
