4 papers
Towards a geometric theory of integration
Filip Bár
Integration is the final key step when turning an infinitesimal argument into a result applicable to quantities of finite size. Conceptually, it is about combining infinitesimal co…
The Fundamental Theorem of Calculus in higher dimensions
Filip Bár
We generalise the Fundamental Theorem of Calculus to higher dimensions. Our generalisation is based on the observation that the antiderivative of a function of -variables is a s…
Gluing of infinitesimal models of algebraic theories
Filip Bár
Categories of models of algebraic theories have good categorical properties except for gluing. Building upon insights and examples from Synthetic Differential Geometry, we introduc…
Second-order infinitesimal groups and affine connections
Filip Bár
This paper presents new research in infinitesimal algebra by introducing the concept of an infinitesimal group and exploring its properties and ramifications. The author investigat…