COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

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
- CMS Events
- DPMMS info aggregator
- Extraordinary Category Theory Seminar
- Hanchen DaDaDash
- Interested Talks
- MR5, Centre for Mathematical Sciences
- bld31
- ndb35's list
Note that ex-directory lists are not shown. |
## Other listsPharmacology Tea Club seminars Qatar Carbonates and Carbon Storage Research Centre: Status update after three years of fundamental research anthropology Dr Chang Zhang Combinatorics Seminar Hitachi Cambridge Seminar Series## Other talksUnderstanding and Estimating Physical Parameters in Electric Motors using Mathematical Modelling The Move of Economics Ideas and Numbers into Policy Recent Changes of Korean Government's Strategy on back-end fuel cycle and the changing course of a University Laboratory What is the History of the Book? Transcriptional control of pluripotent stem cell fate by the Nucleosome Remodelling and Deacetylation (NuRD) complex The homelands of the plague: Soviet disease ecology in Central Asia, 1920s–1950s |