Title: Integral Category Structure of Smooth Functions Abstract: In this talk, I will explain how line integration from classical vector calculus gives an integral combinator on the category of real smooth functions.

# Event categories Archives:

## Jonathan Gallagher

Title: Scott, Koymans, and Beyond Abstract: Dana Scott, in "Relating theories of the lambda calculus" sought to show that the same techniques for modelling the simply typed lambda calculus can be used to model the untyped lambda calculus. He essentially constructed an adjunction between lambda theories T and cartesian closed categories X with a chosen […]

## Jonathan Gallagher

Title: A tutorial on the Scott--Koymans [*] theorem part 2 Abstract: We will continue our investigation into the modernization of the Scott-Koymans theorem. This theorem says, roughly, that the semantics of the untyped lambda calculus into CCCs with a reflexive object, is sound and complete -- in fact it says: Theorem: Every lambda theory T, has […]

## Daniel Satanove

Title: Internal Full Subcategories Abstract: This talk will introduce the notion of an internal category as a certain kind of object in a category. The goal of this talk is to examine what it means for a category in X to be a full subcategory of X.

## Matthew Burke

Title: Lie’s Third Theorem using an Intuitionistic Double Negation Abstract: In this talk we will describe the construction of a local approximation of category in a certain well adapted model of synthetic differential geometry. This approximation is analogous to the germ of a local Lie group and is constructed using an intuitionistic double negation. After […]

## Priyaa Srinivasan

Title: Environment structures for dagger compact closed categories Abstract: In this talk, I will introduce environment structure for a dagger compact closed category and purification for an environment structure. I will provide an example environment structure in the category of Hilbert spaces and completely positive maps. I will also prove the following theorem: Suppose C […]

## Matthew Burke

Title: Sites of Smooth Affine Schemes Abstract: In this talk we will sketch the construction of a few well-adapted models of synthetic differential geometry. Then we will recall the definition of an intuitionistic order relation and show how to define one in the Dubuc topos. Finally we will formulate Lie’s third theorem in a manner […]

## Matthew Burke and Ben MacAdam

Talk 1: Speaker: Matthew Burke Title: Sites of Smooth Affine Schemes Abstract: In this talk we will sketch the construction of a few well-adapted models of synthetic differential geometry. Then we will recall the definition of an intuitionistic order relation and show how to define one in the Dubuc topos. Finally we will formulate Lie’s […]

## Matthew Burke

## Jonathan Gallagher

Speaker: Jonathan Gallagher Title: Ditching squares for triangles -- confluence in under an hour Abstract: In this talk, we will give a proof of the Church-Rosser theorem for the lambda-calculus that is due to Takahashi 1995. Takashi used a property of developments -- that they are always developing towards a 'goal' -- to give the […]