Fields of geometry refer to the various branches and areas of study within the broader field of geometry, which is a branch of mathematics concerned with the properties and relationships of points, lines, shapes, and spaces. Here are several key fields within geometry: 1. **Euclidean Geometry**: The study of flat spaces and figures, based on the postulates laid out by the ancient Greek mathematician Euclid. It includes concepts like points, lines, angles, triangles, circles, and polygons.
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.