The rôle of categorical structures in infinitesimal calculus

izvorni znanstveni rad

izvorni znanstveni rad

The rôle of categorical structures in infinitesimal calculus

Vrsta prilog u časopisu
Tip izvorni znanstveni rad
Godina 2013
Časopis Journal of applied mathematics and computational mechanics
Nadređena publikacija Journal of Applied Mathematics and Computational Mechanics
Volumen 12
Svesčić 1
Stranice str. 107-119
DOI 10.17512/jamcm.2013.1.11
ISSN 2299-9965
EISSN 2353-0588
Status objavljeno

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.

Ključne riječi

categorical structures ; cathegory theory ; infinitesimal calculus