暇つぶし2chat MATH

- 暇つぶし2ch317:んで対比するのが良いと思う https://en.wikipedia.org/wiki/Outline_of_category_theory Outline of category theory (抜粋) The following outline is provided as an overview of and guide to category theory, the area of study in mathematics that examines in an abstract way the properties of particular mathematical concepts, by formalising them as collections of objects and arrows (also called morphisms, although this term also has a specific, non category-theoretical sense), where these collections satisfy certain basic conditions. Many significant areas of mathematics can be formalised as categories, and the use of category theory allows many intricate and subtle mathematical results in these fields to be stated, and proved, in a much simpler way than without the use of categories. Contents 1 Essence of category theory 2 Branches of category theory 3 Specific categories 4 Objects 5 Morphisms 6 Functors 7 Limits 8 Additive structure 9 Dagger categories 10 Monoidal categories 11 Cartesian closed category 12 Structure 13 Topoi, toposes 14 History of category theory 15 Persons influential in the field of category theory Essence of category theory Category ? Functor ? Natural transformation ? Branches of category theory Homological algebra ? Diagram chasing ? Topos theory ? Enriched category theory ? Higher category theory ? Additive structure Derived category ? Triangulated category ? Model category ? 2-category ? Cartesian closed category Topos Topoi, toposes Sheaf ? Gluing axiom ? Descent (category theory) ? Grothendieck topology ?