文档介绍：Category Theory (Stanford Encyclopedia of Philosophy) -theory/
Open access to the SEP is made possible by a world-wide funding initiative.
Please Read How You Can Help Keep the Encyclopedia Free
Category Theory
First published Fri Dec 6, 1996; substantive revision Thu Aug 30, 2007
Category theory e to occupy a central position in contemporary mathematics
and puter science, and is also applied to mathematical physics.
Roughly, it is a general mathematical theory of structures and of systems of structures.
As category theory is still evolving, its functions are correspondingly developing,
expanding and multiplying. At minimum, it is a powerful language, or conceptual
framework, allowing us to see the ponents of a family of structures of a
given kind, and how structures of different kinds are interrelated. Category theory is
both an interesting object of philosophical study, and a potentially powerful formal
tool for philosophical investigations of concepts such as space, system, and even truth.
It can be applied to the study of logical systems in which case category theory is
called "categorical doctrines" at the syntactic, proof-theoretic, and semantic levels.
Category theory is an alternative to set theory as a foundation for mathematics. As
such, it raises many issues about mathematical ontology and epistemology. Category
theory thus affords philosophers and logicians much to use and reflect upon.
1. General Definitions, Examples and Applications
2. Brief Historical Sketch
3. Philosophical Significance
Bibliography
Other Resources
Related Entries
1. General Definitions, Examples and Applications
Definitions
Categories are algebraic structures with plementary natures, ., geometric,
logical, computational, combinatorial, just as groups are many-faceted algebraic
structures. Eilenberg & Mac Lane (1945) introduced categories in a purely auxiliary
fashion, on