6 citations · 16 across the 5 of their papers we have counts for
7 papers · 1 filter
Pregroupoids and their enveloping groupoids
Anders Kock
We prove that the forgetful functor from groupoids to pregroupoids has a left adjoint, with the front adjunction injective. Thus we get an enveloping groupoid for any pregroupoid.…
Categorical distribution theory; heat equation
Anders Kock, Gonzalo E. Reyes
The aim of this paper is to develop the theory of distributions, not necessarily of compact support, in a topos model of Synthetic Differential Geometry, the so-called "Cahiers Top…
Some calculus with extensive quantities: wave equation
Anders Kock, Gonzalo E. Reyes
We take some first steps in providing a synthetic theory of distributions. In particular, we are interested in the use of distribution theory as foundation, not just as tool, in th…
Some differential equations in synthetic differential geometry
Anders Kock, Gonzalo E. Reyes
Some differential equations are considered in the context of Synthetic Differential Geometry. Here, this means that not only nilpotent infinitesimals, but also the formation of fun…
Infinitesimal aspects of the Laplace operator
Anders Kock
In the context of synthetic differential geometry, we study the Laplace operator an a Riemannian manifold. The main new aspect is a neighbourhood of the diagonal, smaller than the…
Volume form as volume of infinitesimal simplices
Anders Kock
In the context of Synthetic Differential Geometry, we describe the square volume of a ``second-infinitesimal simplex'', in terms of square-distance between its vertices. The square…