Fuzzy Conifold Y_F⁶ and Monopoles on S_F²times S_F²

In this article, we construct the fuzzy (finite dimensional) analogues of the conifold $Y^6$ and its base $X^5$. We show that fuzzy $X^5$ is (the analogue of) a principal U(1) bundle over fuzzy spheres $S^2_F \times S^2_F$ and explicitly construct the associated monopole bundles. In particular our construction provides an explicit discretization of the spaces $T^{\kappa,\kappa}$ and $T^{\kappa,0}$.