Matías Menni (Univeristy of La Plata) will teach a short course in Salerno on Axiomatic Cohesion. Further details are given below.
An introduction to Axiomatic Cohesion.
Brief description of the course
The seminal paper reprinted in [L5] proposes to axiomatize the “distinctive internal connectedness of a topos that models all spaces of a ‘general’ combinatorial, algebraic, or smooth kind”.
In the Author Commentary of [L5], Lawvere observes that “The simple idea at the core of this paper has not yet been much pursued by workers in topos theory” and, in [L7], he reformulates the proposal, including several new concepts, problems and conjectures. This reformulation incited further work starting with [J11] and continued by others, including Marmolejo, Menni and Lawvere himself.
The purpose of the seminar is to present to the participants the fundamental ideas in [L5, L7] and some of their recent developments. More specifically, the objective is that, at the end of the seminar, the participants will be able to apply the axioms for cohesion in their work, and to be aware of many research directions available at present.
References
[J11] Johnstone, P. T. Remarks on punctual local connectedness. Theory Appl. Categ. 25, 2011.
[L5] Lawvere, F. W. Categories of spaces may not be generalized spaces as exemplified by directed graphs. Repr. Theory Appl. Categ. No. 9, 2005.
[L7] Lawvere, F. W. Axiomatic Cohesion. Theory Appl. Categ. 19, 2007.
[LM15] Lawvere, F. W.; Menni, M. Internal choice holds in the discrete part of any cohesive topos satisfying stable connected codiscreteness. Theory Appl. Categ. 30, 2015.
[MM17] Marmolejo, F.; Menni, M. On the relation between continuous and combinatorial. J. Homotopy Relat. Struct. 12, 2017.
Schedule
All lectures will be in the Sala Riunioni of the Department of Mathematics. The schedule is as follows.
Wednesday, June 4th from 11:00 AM to 12:30 PM
Thursday, June 5th from 11:00 AM to 12:30 PM
Tuesday, June 10th from 11:00 AM to 12:30 PM
Thursday, June 12th from 11:00 AM to 12:30 PM
Wednesday, June 18th from 11:00 AM to 12:30 PM
Remote attendance
It will possible to attend remotely the lectures on Teams. For further information please contact us.
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