Geometric Embedding

A geometric embedding ℱ ↪ ℰ ↪ ℱ ℰ \mathcal{F}\hookrightarrow\mathcal{E} is a Geometric Morphism ( f ∗ : ℱ → ℰ , f ∗ : ℰ → ℱ ) : subscript 𝑓 → ℱ ℰ superscript 𝑓 : → ℰ 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: ℱ ℱ \mathcal{F} is a Reflective Subcategory of ℰ ℰ \mathcal{E} .