Title: Tate's and Yoshida's theorem for fusion systems Authors: A. Dmaz, A. Glesser, S. Park, R. Stancu Abstract: We prove analogues of results of Tate and Yoshida on control of transfer for fusion systems. This requires the notions of p-group residuals and transfer maps in cohomology for fusion systems. As a corollary we obtain a p-nilpotency criterion due to Tate.