Remark

Duality Principle

Category Theory · category.tex

Let $\mathcal{C}$ be a category (Definition~Category). Any statement about $\mathcal{C}$ has a dual statement obtained by replacing

morphisms $f : X \to Y$ by $f : Y \to X$
compositions $g \circ f$ by $f \circ g$

which corresponds precisely to passing to the opposite category $\mathcal{C}^{op}$ defined in Definition~Opposite Category. This observation is called the principle of duality.

Depends on

Category
Opposite Category

Dependency Graph

flowchart LR classDef current fill:#6366f1,color:#fff,stroke:#4f46e5 nf2c6bdf5["Category"] n310ab4af["Opposite Category"] nf3e709f9["Duality Principle"]:::current nf2c6bdf5 --> nf3e709f9 n310ab4af --> nf3e709f9 click nf2c6bdf5 "../objects/f2c6bdf5.html" "_self" click n310ab4af "../objects/310ab4af.html" "_self"