SAKAI Masahiro - 圏論 Diff
- Added parts are displayed like this.
- Deleted parts are displayed
like this.
= 圏論
圏を扱う理論。
== ダイアグラム
((<TeX>))で圏論のダイアグラムを書くには、((<Xy-pic>))が便利。
== 圏論でよく使う文字や記法
((<Unicode>)), 文字実体参照, ((<TeX>)) の場合。
* 合成
* 「{{e '#x2218'}}」「U+2218 (RING OPERATOR)」「\circ」
* PDF からコピペすると 「{{e '#x25e6'}}」「U+25E6 WHITE BULLET」になっていることも。
* 同型
* 「{{e 'cong'}}」「U+2245」「≅」「\cong」
* 極限
* 「\varprojlim_I」
* 余極限
* 「\varinjlim_J」
* 随伴
* 「{{e '#x22a3'}}」「U+22a3」 「\dashv」
== 概念メモ
=== LFP(Locally Finitary Presentable) category
cocomplete category K is called LFP provided that it has a set A of objects B that are finitely presentable (i.e. such that hom(B,-): K->Set preserves filtered colimitis) such that every object is a filtered colimit of objects in A. In such a category every object K is fully described by the hom-sets hom(B,K) for B∈A.
== リンク
* ((<Category Theory (sampou.org)|URL:http://www.sampou.org/cgi-bin/haskell.cgi?CategoryTheory>))
* ((<圏論勉強会|URL:http://www.sampou.org/cgi-bin/haskell.cgi?CategoryTheory%3a%b7%f7%cf%c0%ca%d9%b6%af%b2%f1>))
* ((<"ヒビルテ:圏論"|URL:/d/?category=%B7%F7%CF%C0>))"|URL:/d/?category=%E5%9C%8F%E8%AB%96>))
* ((<URL:http://plato.stanford.edu/entries/category-theory/>))
* ((<URL:http://www.tac.mta.ca/tac/>))
* ((<URL:http://coolee.at.infoseek.co.jp/kenron.html>))
* ((<URL:http://www.andrew.cmu.edu/course/80-413-713/notes/cats.pdf>))
* ((<An ABC of Category Theory|URL:http://www.maths.gla.ac.uk/~tl/ct/>))
圏を扱う理論。
== ダイアグラム
((<TeX>))で圏論のダイアグラムを書くには、((<Xy-pic>))が便利。
== 圏論でよく使う文字や記法
((<Unicode>)), 文字実体参照, ((<TeX>)) の場合。
* 合成
* 「{{e '#x2218'}}」「U+2218 (RING OPERATOR)」「\circ」
* PDF からコピペすると 「{{e '#x25e6'}}」「U+25E6 WHITE BULLET」になっていることも。
* 同型
* 「{{e 'cong'}}」「U+2245」「≅」「\cong」
* 極限
* 「\varprojlim_I」
* 余極限
* 「\varinjlim_J」
* 随伴
* 「{{e '#x22a3'}}」「U+22a3」 「\dashv」
== 概念メモ
=== LFP(Locally Finitary Presentable) category
cocomplete category K is called LFP provided that it has a set A of objects B that are finitely presentable (i.e. such that hom(B,-): K->Set preserves filtered colimitis) such that every object is a filtered colimit of objects in A. In such a category every object K is fully described by the hom-sets hom(B,K) for B∈A.
== リンク
* ((<Category Theory (sampou.org)|URL:http://www.sampou.org/cgi-bin/haskell.cgi?CategoryTheory>))
* ((<圏論勉強会|URL:http://www.sampou.org/cgi-bin/haskell.cgi?CategoryTheory%3a%b7%f7%cf%c0%ca%d9%b6%af%b2%f1>))
* ((<"ヒビルテ:圏論
* ((<URL:http://plato.stanford.edu/entries/category-theory/>))
* ((<URL:http://www.tac.mta.ca/tac/>))
* ((<URL:http://coolee.at.infoseek.co.jp/kenron.html>))
* ((<URL:http://www.andrew.cmu.edu/course/80-413-713/notes/cats.pdf>))
* ((<An ABC of Category Theory|URL:http://www.maths.gla.ac.uk/~tl/ct/>))