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# Topology Seminar

**
Mon., Dec. 5, 2022 1:00 p.m.
**

**
Location: CL 312
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**Speaker: **Manak Singh

**Title: **The Grothendieck spectral sequence

**Abstract: **

Suppose F : A → B and G : B → C are left exact functors between abelian categories, where A and B have enough injectives. For each object of A, given some extra conditions on F and G, there exists a convergent spectral sequence called the Grothendieck spectral sequence (GSS), which tells us how to compose the right derived functors of F and G, in order to get the right derived functors of GF. I prove the theorem by Grothendieck that encapsulates this property. I also briefly provide a context in which a GSS is constructed.