# Math

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

Materials Category Theory by Steve Awodey Very kind “Category Theory For Beginners” by Richard Southwell. My memo: Introduction done My memo: Functor done Definition of a category Objects and arrows exist. There should be identity arrows for all objects. Arrows should be composited. Associativity holds. Terminology: domain and codomain $\mathrm{dom}(f)\xrightarrow{f} \mathrm{cod}(f)$ Directed graphs and categories If $f:A\rightarrow B$ and $g:B\rightarrow C$ exist but $h := g\cdot f$ doesn’t, it violates the rule of composition.