diff --git a/trees/cat-0004.tree b/trees/cat-0004.tree new file mode 100644 index 0000000..38592b1 --- /dev/null +++ b/trees/cat-0004.tree @@ -0,0 +1,12 @@ +\title{cartesian closed category} +\taxon{definition} +\author{dannypsnl} +\date{2023-10-24} + +\p{ + 一個[範疇](cat-0001) #{C} 被稱為 cartesian closed 表示 + \ol{ + \li{任意有限多個 objects #{\{a_i \mid i \in \mathbb{N}\}} 的 product #{a_0 \times ... \times a_n} 亦是範疇的 object} + \li{對所有 object #{a \in C} 而言,functor #{a \times - : C \to C} 是 #{(-)^a : C \to C} 的[右伴隨](https://en.wikipedia.org/wiki/Adjoint_functors)} + } +}