MTL728: Category Theory

3 Credits (3-0-0)

Categories, functors and natural transformations, adjoints (of functors), representable functors, Yoneda Lemma and applications. Limits and colimits, interaction between functors and limits. Limits in terms of representables and adjoints, limits and colimits of presheaves, interaction between adjoint functors and limits. Application to abelian category: complexes of R-modules, long exact sequence, mapping cone and cylinder, projective and injective resolution, derived functors, right and left exactness, Ext and Tor. Concept of presheaf and sheaf, group scheme and Hopf algebra.