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