Christoph Dorn

Mathematician and computer scientist. Interested in computable foundations of geometry and higher algebra.

Framed Combinatorial Topology

Framed combinatorial topology is a novel theory describing combinatorial phenomena arising at the intersection of stratified topology and higher algebra.

Here’s a page that collects basic ideas and material about the subject.

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Principles of higher-dimensional logic

Comments first published

We allow ourselves to speculate a bit about how the 1-dimensional logical constructs that one frequently encounters in practical approaches to mathematical foundations may in fact emerge from a set of “more fundamental” principles of compositionality in higher-dimensional logic. → read note

Towards computable manifolds

Comments first published

In this (exceedingly brief) note, we discuss computability questions in the context of manifold theory. The main observation is that several computabilty issues in classical “set-point (differential) topological” foundations may potentially be overcome when working with manifolds from the higher-categorical perspective of manifold diagrams and tangles. → read note

The $D_4$ dualizability law

Comments first published

This note gives a brief visual guide to how one can understand the classical \(D_4\) singularity in terms of a categorical pasting diagram (aka manifold diagram, or more specifically, a tame tangle). → read note