From 7c0e93689d24ae4d6759ba2f6e9159a9131cdbd2 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?L=C3=AEm=20Ts=C3=BA-thu=C3=A0n?= Date: Tue, 24 Oct 2023 01:51:22 +0800 Subject: [PATCH 1/2] cartesian closed category MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Signed-off-by: Lîm Tsú-thuàn --- trees/cat-0004.tree | 12 ++++++++++++ 1 file changed, 12 insertions(+) create mode 100644 trees/cat-0004.tree diff --git a/trees/cat-0004.tree b/trees/cat-0004.tree new file mode 100644 index 0000000..94118f6 --- /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} + } +} From dd17d1ecd83f48818dd529a7baa421b2a0802ac1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?L=C3=AEm=20Ts=C3=BA-thu=C3=A0n?= Date: Wed, 25 Oct 2023 23:20:28 +0800 Subject: [PATCH 2/2] =?UTF-8?q?wiki=20=E5=85=88=E9=A0=82=E8=91=97?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Signed-off-by: Lîm Tsú-thuàn --- trees/cat-0004.tree | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/trees/cat-0004.tree b/trees/cat-0004.tree index 94118f6..38592b1 100644 --- a/trees/cat-0004.tree +++ b/trees/cat-0004.tree @@ -7,6 +7,6 @@ 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} + \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)} } }