# Math

### Category Theory (Apr.2021. updating continuously)

Materials Category Theory by Steve Awodey Very kind “Category Theory For Beginners” by Richard Southwell. Definition of a category Objects and arrows are there. There should be identity arrows. Arrows should be composited. Associativity holds. Terminology: domain and codomain $\mathrm{dom}(f)\xrightarrow{f} \mathrm{cod}(f)$ Functor A Functor is a mapping between categories. It’s like an arrow from category to category. It preseves compositions $F(g\cdot f) = F(g)\cdot F(f)$. Identitiy arrows are mapped to identity arrows.