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Classical Control, Quantum Circuits and Linear Logic in Enriched Category Theory [PDF]

Logical Methods in Computer Science, 2020
We describe categorical models of a circuit-based (quantum) functional programming language. We show that enriched categories play a crucial role. Following earlier work on QWire by Paykin et al., we consider both a simple first-order linear language for
Mathys Rennela, Sam Staton
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Lifting Coalgebra Modalities and $\mathsf{MELL}$ Model Structure to Eilenberg-Moore Categories [PDF]

Logical Methods in Computer Science, 2019
A categorical model of the multiplicative and exponential fragments of intuitionistic linear logic ($\mathsf{MELL}$), known as a \emph{linear category}, is a symmetric monoidal closed category with a monoidal coalgebra modality (also known as a linear ...
Jean-Simon Pacaud Lemay
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Sampled-data fuzzy $$H_\infty$$ estimators for control of nonlinear parabolic partial differential equations [PDF]

Scientific Reports
This study handles the robust sampled-data $$H_\infty$$ fuzzy control analysis for a category of nonlinear partial differential systems (NPDSs) holding disturbances.
M. Sivakumar, S. Dharani, Jinde Cao
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Exact Sequences and Closed Model Categories [PDF]

Applied Categorical Structures, 2009
For every closed model category with zero object, Quillen gave the construction of Eckman-Hilton and Puppe sequences. In this paper, we remove the hypothesis of the existence of zero object and construct (using the category over the initial object or the category under the final object) these sequences for unpointed model categories.
Pinillos, M.G., Paricio, L.J.H., Rodríguez, M.T.R.   +2 more
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Ambiguity and Incomplete Information in Categorical Models of Language [PDF]

Electronic Proceedings in Theoretical Computer Science, 2017
We investigate notions of ambiguity and partial information in categorical distributional models of natural language. Probabilistic ambiguity has previously been studied using Selinger's CPM construction.
Dan Marsden
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A Linear Category of Polynomial Functors (extensional part) [PDF]

Logical Methods in Computer Science, 2014
We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is reminiscent ...
Hyvernat Pierre
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A closed model structure on the category of weakly unital dg categories, II

Theory and Applications of Categories, 2021
In this paper, which is subsequent to our previous paper [PS] (but can be read independently from it), we continue our study of the closed model structure on the category $\mathrm{Cat}_{\mathrm{dgwu}}(\Bbbk)$ of small weakly unital dg categories (in the sense of Kontsevich-Soibelman [KS]) over a field $\Bbbk$.
Panero, Piergiorgio, Shoykhet, Boris
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A closed model category for (𝑛-1)-connected spaces [PDF]

Proceedings of the American Mathematical Society, 1996
For each integer n > 0 n > 0 , we give a distinct closed model category structure to the category of pointed spaces Top ⋆ \operatorname {Top}_\star such that the corresponding localized category Ho ⁡ ( Top ⋆ n
Aldana, J.I.E., Paricio, L.J.H., Rodríguez, M.T.R.   +2 more
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The closed model structure on the category of weakly unital dg categories: an addendum

Theory and Applications of Categories, 2022
Weakly unital DG-categories were introduced by \textit{M. Kontsevich} and \textit{Y. Soibelman} [Lect. Notes Phys. 757, 153--219 (2009; Zbl 1202.81120)]. The present authors, in the paper [Theory Appl. Categ. 37, 388--417 (2021; Zbl 1461.18016)] for which the paper under review is an addendum, did as the title implies. However, two results were assumed
Panero, Piergiorgio, Shoykhet, Boris
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An interpretation of dependent type theory in a model category of locally cartesian closed categories [PDF]

Mathematical Structures in Computer Science, 2021
Abstract Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the “gros” semantics in the category of lcc categories: Instead of constructing an interpretation in a given individual lcc category, we show that also the category of all lcc categories can be endowed with ...
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