Talk 6: Sheaves and sheaf cohomology
Marlon Kocher (Universität Heidelberg)

[2, Section 6.2.2 in particular Remark 6.2.2.3] Explain Grothendieck topologies and infinty categorical context. If time permits, mention that, there is a difference between “sheaves on some Grothendieck site” and ∞-topoi, but don’t dwell on this too much. Ellaborate on Remark 6.2.2.3 which asserts that the classical notion of Grothendieck topologies defines a Grothendieck topology on the nerve.
Explain how to compute “sheaf cohomology” using Eilenberg–Maclane objects and how this relates to classical sheaf cohomology (cf. [2, Remark 7.2.2.17]). See also [9] and the nLab article on abelian sheaf cohomology.