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University of Cambridge > Talks.cam > Extraordinary Category Theory Seminar > Hypercovers and factorisation systems in higher categories

## Hypercovers and factorisation systems in higher categoriesAdd to your list(s) Download to your calendar using vCal - Alexander Campbell (Macquarie University)
- Tuesday 25 August 2015, 14:15-15:15
- MR5, Centre for Mathematical Sciences.
If you have a question about this talk, please contact Zhen Lin Low. Grothendieck’s plus construction sends a presheaf F to the presheaf of equivalence classes of “matching families” of elements of F; two iterations yield the associated sheaf of F (n + 2 iterations are generally required for n-stacks). This construction involves colimits over covers. If we instead take colimits over hypercovers, only one iteration is required (for all n); this corresponds to taking equivalence classes of “locally matching famillies” of elements. A similar construction appears in Verdier’s hypercovering theorem on abelian sheaf cohomology. In this talk I will give an account of hypercovers within the higher categorical theory of non-abelian cohomology introduced in my previous talk. I will define (n-)hypercovers over a site to be the indexed n-functors which are locally k-surjective for all k in { 0, 1, ..., n }. These maps form the left class of a factorisation system which will allow us to see the plus construction over hypercovers as another generalised Lawvere construction; for the presheaf case the relevant hypercovers are the locally eso and locally full functors. I will also compare this approach to the simplicial theory of hypercovers. This talk is part of the Extraordinary Category Theory Seminar series. ## This talk is included in these lists:- All CMS events
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