# Algebraic Analysis notes Lecture 11 (4 Feb 2019)

Notes for lecture 10 Last time: for an abelian category A, C(A) is the category of complexes in A. Say $latex f, g \in \mathrm{Hom}_{C(A)} (X, Y)$ are homotopic, f~g, if there are maps $latex s^i : X^i \to Y^i$ such that $latex f^i -g^i = d_Y s + sd_X$. Definition The homotopy category K(A) … Continue reading Algebraic Analysis notes Lecture 11 (4 Feb 2019)

# Algebraic Analysis notes Lecture 10 (1 Feb 2019)

Notes for lecture 9 Last time: $latex \Gamma : Sh(X; k) \to k-mod$ global sections functor is left exact. We'll leave sheaves for now to look at derived categories. What do sheaves have to do with cohomology? Poincare Lemma: Let M be a manifold. Consider the following complex of sheaves: where d is the de … Continue reading Algebraic Analysis notes Lecture 10 (1 Feb 2019)