Title: Exponential Functions for Cartesian Differential Categories. Abstract: We introduce differential exponential maps in Cartesian differential categories, which generalizes the exponential function from classical differential calculus. In particular, differential exponential maps can be defined without the need for limits, converging power series, multiplication, or unique solutions of certain differential equations -- which most Cartesian differential […]

# Event categories Archives:

## Benjamin Macadam

Title: Bertram’s Lie Calculus Abstract: We will consider Bertram’s Lie Calculus, which develops the foundations of differential calculus and Lie theory concurrently. In particular, we shall consider his presentation of Connes’ Tangent Groupoid on the category of smooth manifolds and consider how this could relate to a categorical semantics for identity types.

## Daniel Satanove

Title: Generalized sketches with monad sorts Abstract: I give a generalization of sketches which captures the theories of group presentations and certain notions of generalized multicategories. I conjecture that the categories of models of these sorts of sketches are locally finitely presentable, so that therefore this generalization stays within the realm of essentially algebraic theories.

## Ben MacAdam

Title: Kock-Lawvere Modules in a Tangent Category Abstract: In the category of smooth manifolds, vector spaces have the property that T(V) is isomorphic VxV. When moving to abstract settings for differential geometry, such as synthetic differential geometry, this need not be the case, especially tangent categories without any sort of ring object. Cockett and Cruttwell […]

## Matthew Burke

Title: Involution algebroids and their homotopy theory II Abstract: We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. We first sketch the relationship between our new definition and the classical one. Then as an illustrative example of how to work with the new definition we develop some of the […]

## Matthew Burke

Title: Involution algebroids and their homotopy theory Abstract: We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. We first sketch the relationship between our new definition and the classical one. Then as an illustrative example of how to work with the new definition we develop some of the homotopy […]

## Priyaa Srinivasan

Title: Dagger linear logic for categorical quantum mechanics Abstract: Categorical quantum mechanics is largely based on dagger compact closed categories. A well-known limitation of this approach is that, while it supports finite dimensional processes, it does not generalize well to infinite dimensional processes. A natural categorical generalization of compact closed categories, in which to seek […]

## Rachel Hardeman

Title: Cubical Sets and A-Homotopy Theory Abstract: In this talk, I will describe the cubical category and cubical sets. Then I will show how A-homotopy theory, a discrete homotopy theory for graphs, gives us an example of a cubical set. Time permitting, I will discuss how this cubical set might lead us to a chain […]

## Priyaa Srinivasan

## Geoff Vooys

Title: A Topology on Categories of Locally Ringed Space and Applications to Arithmetic Geometry Abstract: In this talk we present some relevant background on locally ringed spaces and consider a problem that appears in arithmetic geometry. We then use this problem to motivate a class of functors that arise in arithmetic geometry, provide examples of […]