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- Anders Kock
- 2005

- ANDERS KOCK
- 1996

We analyze the Bianchi Identity as an instance of a basic fact of com-binatorial groupoid theory, related to the Homotopy Addition Lemma. Here it becomes formulated in terms of 2-forms with values in the gauge group bundle of a groupoid, and leads in particular to the (Chern-Weil) construction of characteristic classes. The method is that of synthetic… (More)

- Anders Kock
- 2007

- ANDERS KOCK, Michael Barr
- 1998

In terms of synthetic differential geometry, we give a variational characterization of the connection (parallelism) associated to a pseudo-Riemannian metric on a manifold.

- Anders Kock
- 2009

- ANDERS KOCK
- 2012

It is shown how the theory of commutative monads provides an axiomatic framework for several aspects of distribution theory in a broad sense, including probability distributions, physical extensive quantities, and Schwartz distributions of compact support. Among the particular aspects considered here are the notions of convolution, density, expectation, and… (More)

- ANDERS KOCK
- 2000

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 second neighbourhood usually required as support for second order differential operators. The new neighbourhood has the property that a function is affine on it if and only if it… (More)

- ANDERS KOCK
- 2005

In [4] we proved that a commutative monad on a symmetric monoidal closed category carries the structure of a symmetric monoidal monad ([4], Theorem 3.2). We here prove the converse, so that, taken together, we have: there is a 1-1 correspondence between commutative monads and symmetric monoidal monads (Theorem 2.3 below). The main computational work needed… (More)

In the context of constructive locale or frame theory (locale theory over a xed base locale), we study some aspects of 'frame distributions', meaning sup preserving maps from a frame to the base frame. We derive a relationship between results of Jibladze-Johnstone and Bunge-Funk, and also descriptions in distribution terms, as well as in double negation… (More)

- Anders Kock, Max Kelly
- 1991