Geometric Embedding

A geometric embedding \mathcal{F}\hookrightarrow\mathcal{E} is a Geometric Morphism ( f : , f : ) : subscript 𝑓 superscript 𝑓 : (f_{*}:\mathcal{F}\to\mathcal{E},f^{*}:\mathcal{E}\to\mathcal{F}) such that the Right Adjoint f subscript 𝑓 f_{*} is Fully Faithful; EG: \mathcal{F} is a Reflective Subcategory of \mathcal{E} .