Definition:Exponential (Category Theory)/Transpose
Jump to navigation
Jump to search
Definition
Let $\mathbf C$ be a metacategory with binary products.
Let $B$ and $C$ be objects of $\mathbf C$.
Let $C^B$ be an exponential of $C$ by $B$, with evaluation morphism $\epsilon: C^B \times B \to C$.
For a morphism $f: A \times B \to C$, the unique:
- $\tilde f: A \to C^B$
provided by the UMP for $C^B$ is called the exponential transpose of $f$.
For a morphism $g: A \to C^B$, the morphism $\bar g: A \times B \to C$ defined by:
- $\bar g = \epsilon \circ \paren {g \times \operatorname{id}_B}$
is also called the exponential transpose of $g$.
Also see
Sources
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |