Title: Cartan Calculus for Tangent Categories 2 Abstract: We develop the string calculus for Cartesian Tangent categories, and consider the shuffle operation and Noether’s theorem in a tangent category.

# Event categories Archives:

## Matthew Burke

Title: A Two Dimensional Setting for the Calculus of Infinity Functors Abstract: In this talk we combine two related approaches to the theory of infinity categories. On the one hand we use derivators to work with (homotopy) (co)limits within small infinity categories. Using this theory we define the excisive functors, suspension functors etc.. that are […]

## Priyaa Srinivasan

Title: Quantum Channels for Mixed Unitary Categories Abstract: Categorically, quantum processes are modelled as completely positive maps in dagger compact closed categories [1,2,3]. The limitation however is that the quantum processes modelled are for finite-dimensional systems. A natural setting for quantum processes between infinite dimensional systems is a *-autonomous category or more generally a linearly […]

## Cole Comfort

Title: A Complete Classification of the Toffoli Gate with Ancillary bits (second attempt) Abstract: We provide a complete set of identities for the symmetric monoidal category, TOF, generated by the Toffoli gate and computational ancillary bits. We do so by demonstrating that the functor which evaluates circuits on total points is an equivalence into the […]

## Ben MacAdam

Title: Cartan’s calculus for Sector Forms Abstract: Cartan’s calculus of differential forms refers to a collection of operators on differential forms - the exterior derivative, Lie derivative, and interior product - and identities that they satisfy. The calculus of forms is particularly useful in mechanics. In this talk, we show that Cartan’s calculus of forms […]

## Rachel Hardeman

Title: An Introduction to A-Homotopy Theory: A Discrete Homotopy Theory for Graphs Abstract: A-homotopy Theory was invented by Ron Aktin in the 1970s and further developed by Helene Barcelo in the early 2000s as a combinatorial version of homotopy theory. This theory respects the structure of a graph, distinguishing between vertices and edges. While in […]

## Matthew Burke

Title: Free co-completion, presheaves and sheaves Abstract: In response to a special request this talk describes some fundamental aspects of sheaf theory. First we introduce the algebra of ends and co-ends for the purpose of making our subsequent calculations more concrete. Then we describe how the construction of a presheaf category of a small category […]

## Jonathan Gallagher

Title: Frolicher spaces, Weil spaces, Diffeological spaces and abstract differential geometry Abstract: In differential geometry, obtaining a smooth structure on spaces of smooth maps is a motivation for the introduction of various kinds of generalized smooth spaces. Frechet manifolds do allow a manifold structure on the space of smooth maps between *finite* dimensional smooth manifolds, […]

## Matthew Burke

Title: Using Postulated Colimits in Coq Abstract: In this talk we define and construct finite colimits in the Coq proof assistant in a context that is similar to the category of sets. First we review without proof the key mathematical ideas involved in the theory of postulated colimits as described in a note of Anders […]

## Matthew Burke

Title: Localisation of Simplicial Presheaf Categories Abstract: In this talk we describe a special case of left Bousfield localisation that is of interest in the calculus of functors. In particular we work in the category of simplicially enriched presheaves of a small category. First we sketch how the classical small object argument constructs factorisations from […]