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Diffeological principal bundles and principal infinity bundles
In this paper, we study diffeological spaces as certain kinds of discrete simplicial presheaves on the site of cartesian spaces with the coverage of...
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Homotopy Sheaves on Generalised Spaces
We study the homotopy right Kan extension of homotopy sheaves on a category to its free cocompletion, i.e. to its category of presheaves. Any...
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Nonparametric Estimations and the Diffeological Fisher Metric
In this paper, first, we survey the concept of diffeological Fisher metric and its naturality, using functorial language of probabilistic morphisms,...
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Čech-De Rham bicomplex in diffeology
We propose a Čech cohomology for diffeological spaces as the Hochschild cohomology of some characteristic gauge monoid. Then, we describe how this...
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Smooth classifying spaces
We develop the theory of smooth principal bundles for a smooth group G , using the framework of diffeological spaces. After giving new examples...
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On Diffeologies for Power Sets and Measures
We consider a differential geometric setting on power sets and Borel algebras. Our chosen framework is based on diffeologies, and we make a link...
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Suitable Spaces for Shape Optimization
The differential-geometric structure of the manifold of smooth shapes is applied to the theory of shape optimization problems. In particular, a...
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Exterior bundles in diffeology
We explore several notions of k -form at a point in a diffeological space, construct bundles of such k -forms, and compare sections of these bundles to...
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Natural differentiable structures on statistical models and the Fisher metric
In this paper I discuss the relation between the concept of the Fisher metric and the concept of differentiability of a family of probability...
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The \(\mathbb {R}\)-local homotopy theory of smooth spaces
Simplicial presheaves on cartesian spaces provide a general notion of smooth spaces. There is a corresponding smooth version of the singular complex...
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Hierarchies of holonomy groupoids for foliated bundles
We give a new construction of the holonomy groupoid of a regular foliation in terms of a partial connection on a diffeological principal bundle of...
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The Orbit Space and Basic Forms of a Proper Lie Groupoid
A classical result in differential geometry states that for a free and proper Lie group action, the quotient map to the orbit space induces an...
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A Framework for Differential Calculus on Persistence Barcodes
We define notions of differentiability for maps from and to the space of persistence barcodes. Inspired by the theory of diffeological spaces, the...
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Mayer–Vietoris Sequence for Differentiable/Diffeological Spaces
The idea of a space with smooth structure is a generalization of an idea of a manifold. K. T. Chen introduced such a space as a differentiable space...
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Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing
We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with...
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Smooth functorial field theories from B-fields and D-branes
In the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both...
