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...Synthetic differential geometry an application to einstein s equivalence principle tim de laat bachelor thesis for mathematics and physics astronomy supervisor prof dr n p landsman second reader m h a muger institute astrophysics particle preface this is the result of my project in both aim was give satisfactory rigorous formulation general theory relativity gr terms dierential sdg natural which notion innitesimals very important smooth innitesimal analysis sia mathematical corresponding these it forms entrance are formulated categories topoi as i quite new subjects rst needed study them thoroughly before could start studying besides using reformulate intend introduction will also explain special aspects theories point out contrasts with usual structures assume that has some background reasoning logic abstract algebra classical category not assumed but may make things easier wrote appendix covering basic concise way however should be regarded introductory text supervised by klaas want ...