Definition:Full Subcategory

Definition

Let $\mathbf D$ be a metacategory, and let $\mathbf C$ be a subcategory of $\mathbf D$.

Then $\mathbf C$ is called a full subcategory if and only if the inclusion functor $i: \mathbf C \to \mathbf D$ is full.

Also see

• Definition:Full Functor

Sources

• 1971: Saunders Mac Lane: Categories for the Working Mathematician: Chapter $\text I$ Categories, Functors and Natural Transformations: $\S \text{3}$ Functors

• 2010: Steve Awodey: Category Theory (2nd ed.): Chapter $7$ Naturality: $\S 7.1$ Category of Categories