arXiv subjects

Vincent Schmitt

Publications and source records attributed to Vincent Schmitt.

6 recordsLinked to original sources

arXiv2026

Asset Administration Shell-Based OCL Validation Framework for Model-Based System Engineering

Increasing complexity of modern enterprise systems and the demand for automation and interoperability require consistent and semantically validated models in Model-Based Systems Engineering (MBSE). The Object Constraint Language (OCL) supports formal definition of such constraint validations. However, MBSE models and OCL constraints are typically managed in separate tools, causing manual effort during model constraint application and result interpretation. To address this gap, this paper proposes an approach to managing OCL constraints and their validation results through Asset Administration Shells (a well-established technology for interoperability in enterprise systems). The methodology is demonstrated through a fictional industrial scenario, and to support reproducibility, all artifacts are publicly available in a GitHub repository.

cs.SE↗

arXiv2008

Tensor product for symmetric monoidal categories

We introduce a tensor product for symmetric monoidal categories with the following properties. Let SMC denote the 2-category with objects small symmetric monoidal categories, arrows symmetric monoidal functors and 2-cells monoidal natural transformations. Our tensor product together with a suitable unit is part of a structure on SMC that is a 2-categorical version of the symmetric monoidal closed categories. This structure is surprisingly simple. In particular the arrows involved in the associativity and symmetry laws for the tensor and in the unit cancellation laws are 2-natural and satisfy coherence axioms which are strictly commuting diagrams. We also show that the category quotient of SMC by the congruence generated by its 2-cells admits a symmetric monoidal closed structure.

math.CT↗

arXiv2006

Bisimulations of enrichments

In this paper we show that classical notions from automata theory such as simulation and bisimulation can be lifted to the context of enriched categories. The usual properties of bisimulation are nearly all preserved in this new context. The class of enriched functors that correspond to functionnal bisimulations surjective on objects is investigated and appears "nearly" open in the sense of Joyal and Moerdijk. Seeing the change of base techniques as a convenient means to define process refinement/abstractions, we give sufficient conditions for the change of base categories to preserve bisimularity. We apply these concepts to Betti's generalized automata, categorical transition systems, and other exotic categories.

cs.LO↗

arXiv2006

Flatness, preorders and general metric spaces (revised)

We use a generic notion of flatness in the enriched context to define various completions of metric spaces -- enrichments over [0,\infty] -- and preorders -- enrichments over 2. We characterize the weights of colimits commuting in [0,\infty] with the terminal object and cotensors. These weights can be intrepreted in metric terms as peculiar filters, the so-called filters of type 1. This generalizes Lawvere's correspondence between minimal Cauchy filters and adjoint modules. We obtain a metric completion based on the filters of type 1 as an instance of the free cocompletion under a class of weights defined by G.M. Kelly. Another class of flat presheaves is considered both in the metric and the preorder context. The corresponding completion for preorders is the so-called dcpo-completion.

math.CT↗

arXiv2004

Flatness, accessibility and metric spaces

This paper studies a notion of parameterized flatness in the enriched context: p-flatness where the parameter p stands for a class of presheaves. One obtains a completion of a category A by considering the category F_p(A) of p-flat presheaves over A. The completion is related to the free cocompletion under a class of colimits defined by Kelly. We define a notion of Q-accessible categories where Q is the class of p-flat indexes. For a category A, for p = P0 the class of all presheaves, F_P0(A) is the Cauchy-completion of A. Two classes P1 and P2 of interest for general metric spaces and prorders are considered. The F_P1- and F_P2- flatess are characterized yielding non-symmetric completions of metric spaces a la Cauchy involving non-symmetric filters.

math.CT↗

arXiv2003

Flatness, preorders and general metric spaces

This paper studies a general notion of flatness in the enriched context: P-flatness where the parameter P stands for a class of presheaves. One obtains a completion of a category A by considering the category Flat_P(A) of P-flat presheaves over A. This completion is related to the free cocompletion of A under a class of colimits defined by Kelly. For a category A, for P = P0 the class of all presheaves, Flat_P0(A) is the Cauchy-completion of A. Two classes P1 and P2 of general interest for general metric spaces are considered. The P1- and P2-flatness are investigated and the associated completions are characterized for general metric spaces (enrichemnts over R+) and preorders (enrichments over Bool). We get this way two non-symmetric completions for metric spaces and retrieve the ideal completion for preorders.

math.CT↗