In mathematics, the Oka coherence theorem, proved by Kiyoshi Oka (1950), states that the sheaf ${\displaystyle {\mathcal {O}}_{\mathbb {C} ^{n}}}$ of holomorphic functions on ${\displaystyle \mathbb {C} ^{n}}$ (and subsequently the sheaf ${\displaystyle {\mathcal {O}}_{X}}$ of holomorphic functions on a complex manifold ${\displaystyle X}$) is coherent.