In geometry, a theorem is a statement or proposition that has been proven to be true based on a set of axioms and previously established theorems. Theorems are fundamental to the study of geometry as they provide essential insights and conclusions about geometric figures, relationships, and properties. Theorems in geometry often involve concepts such as points, lines, angles, shapes, and their properties.
Category theory is a branch of mathematics that focuses on the abstract study of mathematical structures and relationships between them. It provides a unifying framework to understand various mathematical concepts across different fields by focusing on the relationships (morphisms) between objects rather than the objects themselves. Here are some key concepts in category theory: 1. **Categories**: A category consists of objects and morphisms (arrows) that map between these objects. Each morphism has a source object and a target object.