Event categories Archives:

Title:  Linearly distributive categories and daggers do mix! Abstract:  We shall explain the basic structure of a dagger *-autonomous category and exhibit a basic example using finiteness spaces.  Time permitting we will discuss how the CPM construction can be generalized to this setting.

Title: The Calculus of Functors using Sheafification Abstract: In classical calculus we approximate an appropriately differentiable function using a sequence of simpler functions called the Taylor polynomials. In an analogous way we can approximate a functor whose domain and codomain are appropriately topological by using a sequence of simpler functors. These simpler functors can be […]

Title: Proving Teleportation protocol using ZX-calculus Abstract: In my previous talks, I introduced environment structures and discarding maps. In this talk I will use discarding maps and ZX- calculus to prove the correctness of teleportation protocol. ZX- calculus is a universal graphical calculus for reasoning about quantum processes. With discarding maps, one can graphically represent […]

Title: Abelian functor calculus, derivatives, and operads Abstract: The first chain rules in functor calculus were established by Arone-Ching and Klein-Rognes, who considered functors of spaces or spectra.  The Arone-Ching chain rule stemmed from earlier work of M. Ching, in which he established that the derivatives of the identity functor form an operad, whose homology […]

[latexpage] Title: A Complete Classification of the Toffoli Gate with Ancillary bits Abstract: The Toffoli gate is a universal gate for classical reversible computation.  This means that if we are allowed to fix the values of certain inputs and outputs (called ancillary bits), we can simulate any Boolean function from $\mathbb{Z}_2^n \to \mathbb{Z}_2^m$ with a […]

[latexpage] Title: A Complete Classification of the Toffoli Gate with Ancillary bits Abstract: The Toffoli gate is a universal gate for classical reversible computation.  This means that if we are allowed to fix the values of certain inputs and outputs (called ancillary bits), we can simulate any Boolean function from $\mathbb{Z}_2^n \to \mathbb{Z}_2^m$ with a […]

[latexpage] Talk 1 - Ben MacAdam Title: Linear/Non-Linear models in a 2-category: Part 1 Abstract: A linear/non-linear model is a monoidal adjunction between a cartesian category and symmetric monoidal category. Such an adjunction gives rise to a coalgebraic modality which in turn a model of MELL.  Birkedal showed that these results translate easily to fibred […]

Title: Differentiation is progressive Abstract: The Takahashi triangle property for abstract rewriting systems contrasts 'good' and 'bad' developments of a simultaneous set of rewrites: for every bad development, there is a better development that converts the result into the result of the good development. Takahashi used the triangle property to study the confluence and standardization […]

[latexpage] Talk 1 - Ben MacAdam Title: Linear/Non-Linear models in a 2-category: Part 1 Abstract: A linear/non-linear model is a monoidal adjunction between a cartesian category and symmetric monoidal category. Such an adjunction gives rise to a coalgebraic modality which in turn is a model of MELL.  Birkedal showed that these results translate easily to […]

We complete the characterization of the simple fibration in an arbitrary 2-category and apply it to define a fibered system of linear maps. Applications to abstract differential geometry and string calculi will be discussed.