A Categorical Theory of Patches

A Categorical Theory of Patches

When working with distant collaborators on the same files, one often uses a distributed version control system, which is a program tracking the history of files and helps importing modifications brought by others as patches. The implementation of such a system requires to handle lots of situations depending on the operations users have performed on files, and it is thus difficult to ensure that...

A Theory of Categorical Terrorism

When revolutionaries or insurgents, broadly defined, indiscriminately attack civilians, they generally attack “complicitous civilians,” i.e., those categories of noncombatants which the revolutionaries see as benefiting from, supporting and/or having a substantial capacity to influence the states that the revolutionaries are attempting to displace or overthrow. Such “categorical” terrorism will...

A Categorical Theory of Hybrid Systems

A Categorical Theory of Hybrid Systems by Aaron David Ames Doctor of Philosophy in Engineering—Electrical Engineering and Computer Sciences University of California, Berkeley Professor Shankar Sastry, Chair This dissertation uses the formalism of category theory to study hybrid phenomena. One begins with a collection of “non-hybrid” mathematical objects that have been well-studied, together wit...

Categorical homotopy theory

Categorical Homotopy Theory

This paper is an exposition of the ideas and methods of Cisinksi, in the context of A-presheaves on a small Grothendieck site, where A is an arbitrary test category in the sense of Grothendieck. The homotopy theory for the category of simplicial presheaves and each of its localizations can be modelled by A-presheaves in the sense that there is a corresponding model structure for A-presheaves wi...