Past meetings
16th meeting - 09 May 2018
Speaker: Paolo Capriotti (video)
Subobject classifier for sheaves. Proof that filtered colimits in \(\mathsf{Set}\) commute with finite limits.
6 participants
15th meeting - 02 May 2018
Speaker: Paolo Capriotti (video)
Review of basic properties of reflective subcategories.
6 participants
14th meeting - 25 Apr 2018
Speaker: Paolo Capriotti (video)
Proof that continuous \(G\)-sets form a Grothendieck topos.
2 participants
13th meeting - 04 Apr 2018
Speaker: Paolo Capriotti (video)
Review of nerve-realisation adjunctions. Filtered colimits in \(\mathsf{Set}\) commute with finite limits. Beginning of the construction of a site for \(G\)-sets.
6 participants
12th meeting - 28 Mar 2018
Speaker: Paolo Capriotti (video)
Review of topological groups. Examples of profinite groups. Infinite permutation groups. Nominal sets.
6 participants
11th meeting - 07 Mar 2018
Speaker: Rafaël Bocquet (video)
Direct image of a monomorphism in a topos.
4 participants
10th meeting - 28 Feb 2018
Speaker: Rafaël Bocquet (video)
Definition of elementary topos. Power objects. Exponentials in elementary topoi.
5 participants
9th meeting - 21 Feb 2018
Speaker: Jakob von Raumer (video)
The "plus" construction of the associated sheaf functor over a general site. Left exactness of the associated sheaf functor.
7 participants
8th meeting - 14 Feb 2018
Speaker: Jakob von Raumer (video)
Grothendieck topologies and sites. Trivial, dense and atomic topologies. Bases of Grothendieck topologies. Sheaves over a site. Limits of sheaves. Sheaves over a base.
5 participants
7th meeting - 07 Feb 2018
Speaker: Paolo Capriotti (video)
Full construction of the adjunction between presheaves and étale bundles. Sheaves as a reflective subcategory of presheaves.
8 participants
6th meeting - 31 Jan 2018
Speaker: Paolo Capriotti (video)
Bundles, locally trivial bundles, vector bundles, covering spaces. Tangent bundle of a manifold. Sheaf of sections of a bundle. Beginning of the construction of the étale bundle of a presheaf.
5 participants
5th meeting - 24 Jan 2018
Speaker: Paolo Capriotti (video)
Sheaves on topological spaces, with various examples and non-examples.
7 participants
4th meeting - 17 Jan 2018
Speaker: Paolo Capriotti (video)
Subobject classifier for various other presheaf categories. General case of subobject classifier for presheaves.
9 participants
3rd meeting - 06 Dec 2017
Speaker: Paolo Capriotti (video)
Continuous actions of infinite permutation groups. Equivalence of the two definitions of subobject classifiers. Subobject classifier for \(M\)-sets.
5 participants
2nd meeting - 29 Nov 2017
Speaker: Paolo Capriotti
Continuous \(G\)-sets, definition and first properties of subobject classifiers, subobject classifiers for \(\mathsf{Set}\), \(\mathsf{Set} \times \mathsf{Set}\) and \(G\)-sets.
9 participants
1st meeting - 22 Nov 2017
Speaker: Paolo Capriotti
Examples of topoi: presheaves, finite sets. Limits in presheaf categories.
10 participants
0th meeting - 15 Nov 2017
Speaker: Paolo Capriotti
Summary of the contents of the book: sheaves, Grothendieck topoi, elementary topoi, classifying topoi, locales, logical aspects of topos theory. Some examples of presheaf categories.
5 participants