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 fibred monoidal categories — here one obtains a model in each fiber category. We show that many of these results can be further generalized to pseudomonoids in 2-categories with suitable universal properties.
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 fibred monoidal categories — here one obtains a model in each fiber category. We show that many of these results can be further generalized to pseudomonoids in 2-categories with suitable universal properties.
Talk 2 – Priyaa Srinivasan
Title: Structures for decoherent
Abstract:
This talk will introduce and develop the structure required for studying
decoherence in certain monoidal categories. Our driving example is a
decoherence structure in ![CP^{*}[\mathsf{FHilb}]](https://quicklatex.com/cache3/3e/ql_b089ed140801e6066f37f1589194e03e_l3.png "Rendered by QuickLaTeX.com")
Our goal is to move towards understanding the following:
Theorem:
Let 
be a dagger compact closed category and 
be a subcategory of that inherits the dagger and compact closed structure. Suppose has a decoherence structure with purification, then there exists an invertible dagger functor from 
such that 
be a dagger compact closed category and be a subcategory of that inherits the dagger and compact closed structure. Suppose has a decoherence structure with purification, then there exists an invertible dagger functor from such that 