ncatlab.org
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nCatLab is a comprehensive, community-edited online encyclopedia for category theory and its applications, offering formal definitions, explanations, examples, and references. It includes topics like tangent spaces and tangent categories, connecting differential geometry with higher-category theory.
More resources on Tangent Spaces
mathworld.wolfram.com
MathWorld is a comprehensive online mathematics encyclopedia from Wolfram Research, offering in-depth articles on a wide range of math topics. Each entry includes definitions, theorems, formulas, figures, and examples with cross-references, making it a solid resource for topics like tangent spaces.
ocw.mit.edu
MIT OpenCourseWare (OCW) provides free, online access to course materials from MIT classes. It includes lecture notes, assignments, exams, syllabi, and often video lectures and readings across a broad range of subjects, including mathematics.