Naslov
The rôle of categorical structures in infinitesimal calculus

Autori
Steingartner, William ; Galinec, Darko

Izvornik
Journal of Applied Mathematics and Computational Mechanics (2299-9965) 12 (2013), 1; 107-119

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
categorical structures ; cathegory theory ; infinitesimal calculus

Sažetak
The development of mathematics stands as one of the most important achievements of humanity, and the development of the calculus, differential calculus and integral calculus is one of the most important achievements in mathematics. Differential calculus is about finding the slope of a tangent to the graph of a function, or equivalently, differential calculus is about finding the rate of change of one quantity with respect to another quantity. On the other hand, integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus. Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. The category theory is a mathematical approach to the study of algebraic structure that has become an important tool in theoretical computing science, particularly for semantics-based research. The notion of a limit in category theory generalizes various types of universal constructions that occur in diverse areas of mathematics. In our paper we illustrate how to represent some parts of infinitesimal calculus in categorical structures.

Izvorni jezik
Engleski

Znanstvena područja
Računarstvo, Informacijske i komunikacijske znanosti

Napomena
This work is the result of the project implementation: Center of Information and Communication Technologies for Knowledge Systems (ITMS project code: 26220120030) supported by the Research & Development
Operational Program funded by the ERDF.

POVEZANOST RADA