Fuzzy category theory describes category-like structures in which potential objects and potential morphisms are respectively objects and morphisms only to a certain degree. This also allows us to look at categories with crisp objects and morphisms from the point of fuzzy set theory without necessarily framing, explicitly or implicitly, the objects or morphisms of a category in a fuzzy way. Building on the work done on functors in fuzzy categories, we further develop the theory until the notion of adjoint functors using the unit and co-unit. We also provide a sufficient condition for a fuzzy functor so that it admits a left adjoint with a certain degree.