*** Write introduction*** Even though for many classical theories the equations of motion
were known first, such as Newton's equations of classical mechanics or Maxwell's equation …

In this paper, we explain how the abstract notion of a differential bundle in a tangent
category provides a new way of thinking about the category of modules over a commutative …

The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is
given by the source vertical tangent bundle restricted to the identity bisection. Its sections …

Tangent categories provide an axiomatic framework for understanding various tangent
bundles and differential operations that occur in differential geometry, algebraic geometry …

We introduce a class of diffeological spaces, called elastic, on which the left Kan extension
of the tangent functor of smooth manifolds defines an abstract tangent functor in the sense of …

This paper describes how to define and work with differential equations in the abstract
setting of tangent categories. The key notion is that of a curve object which is, for differential …

Tangent categories provide a categorical axiomatization of the tangent bundle. There are
many interesting examples and applications of tangent categories in a variety of areas such …

We continue the program of structural differential geometry that begins with the notion of a
tangent category, an axiomatization of structural aspects of the tangent functor on the …

Ehresmann's introduction of differentiable groupoids in the 1950s may be seen as a starting
point for two diverging lines of research, many-object Lie theory (the study of Lie algebroids …

Tangent categories provide a categorical axiomatization of the tangent bundle. There are
many interesting examples and applications of tangent categories in a variety of areas such …