Category of manifolds

The category of manifolds, often denoted as **Man**, is a mathematical structure in category theory that focuses on differentiable manifolds and smooth maps between them. Here are the key components of this category: 1. **Objects**: The objects in the category of manifolds are differentiable manifolds. A differentiable manifold is a topological space that is locally similar to Euclidean space and has a differentiable structure, meaning that the transition maps between local coordinate charts are differentiable.