Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.
Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.
Explores compositions of applications and injectivity conditions in linear algebra, including restriction of applications and combinatorial proof of injections.
Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.
