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workshop_2 [2014/05/27 16:28] mellies |
workshop_2 [2014/05/30 08:45] (current) mellies |
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| * R. Brown (Bangor Univ.) : Intuitions for cubical models of homotopy types | * R. Brown (Bangor Univ.) : Intuitions for cubical models of homotopy types | ||
| * D.-C. Cisinski (Univ. Toulouse) : Univalence for elegant models of homotopy types | * D.-C. Cisinski (Univ. Toulouse) : Univalence for elegant models of homotopy types | ||
| - | * P. Dybjer (TH Chalmers Gothenburg) : What is a model of type theory | + | * P. Dybjer (TH Chalmers Gothenburg) : What is a model of intuitionistic type theory |
| * M. Hofmann (LMU Munich) : Revisiting the categorical interpretation of type theory | * M. Hofmann (LMU Munich) : Revisiting the categorical interpretation of type theory | ||
| * S. Huber (TH Chalmers Gothenburg) : A Model of Type Theory in Cubical Sets | * S. Huber (TH Chalmers Gothenburg) : A Model of Type Theory in Cubical Sets | ||
| Line 45: | Line 45: | ||
| ^Monday 2 June||| | ^Monday 2 June||| | ||
| |10h30-12h00|Per Martin-Löf|//Sample space-time //|| | |10h30-12h00|Per Martin-Löf|//Sample space-time //|| | ||
| - | |14h00-15h30|Peter Dybjer|//What is a model of type theory//| | + | |14h00-15h30|Peter Dybjer|//What is a model of intuitionistic type theory//| |
| |16h00-17h30|Steve Awodey|//Natural Models of Type Theory//| | |16h00-17h30|Steve Awodey|//Natural Models of Type Theory//| | ||
| ^Tuesday 3 June||| | ^Tuesday 3 June||| | ||
| Line 87: | Line 87: | ||
| **Hofmann**\\ | **Hofmann**\\ | ||
| - | //TBA// | + | //Revisiting the categorical interpretation of type theory// |
| **Huber**\\ | **Huber**\\ | ||
| Line 107: | Line 107: | ||
| //Sample space-time// | //Sample space-time// | ||
| - | **Munch**\\ | + | **Munch-Maccagnoni**\\ |
| //Polarities and classical constructiveness// | //Polarities and classical constructiveness// | ||
| - | > | + | > I will recall what constructive can mean in the context of classical logic, as accounted for by double negation translations and control operators in programming. Girard proposed a few years back a classical sequent calculus where negation is strictly involutive (¬¬A = A) by taking formally into account the polarity of connectives. I will show that this idea is very natural from the point of view of control operators, leading us to a natural deduction where negation is involutive (¬¬A ≅ A). One of the main aspect is that we do not consider that composition needs to be associative when the middle map is from positives to negatives. In a second time I will therefore introduce duploids, which characterises this non-associative composition directly, and relate them to adjunctions. |
| **Palmgren**\\ | **Palmgren**\\ | ||