cartesian closed category
1. Definition
Let \(\mathcal{C}\) be a category. Then \(\mathcal{C}\) is said to be cartesian closed, if
- there exists a terminal object
- there exists finite products
- for objects \(X,Y \in \mathrm{Ob}(\mathcal{C})\), there exists an exponential object, (resp. the product \(- \times C\) is a left adjoint)