A peep at knowledge science in a categorical prospect  

作　　者：Ruqian LU 

机构地区：[1]MADIS Key Lab, Research Center of Network Science, Academy of Mathematics and Systems Scince, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Frontiers of Computer Science》2016年第5期767-768,共2页中国计算机科学前沿（英文版）

基　　金：This work has been supported by the National Key Research and Development Program of China （2016YFB1000902）, the Na- tional Natural Science Foundation of China （Grant Nos. 61232015 and 61073023）, and a Tsinghua-Tencent project. The author thanks his students Chaoqun Fei, Yu Huang and Shengluan Hou for their help.

摘　　要：Mathematics and structuralism Since a long time ago, scientists have pursued the idea of assigning each object of science with a structure. In the long run of history, this idea got a loud name of ＂structuralism＂ which received most attention from the mathematicians. The best known early work in ＂structural mathematics＂ was done by the Bourbaki School [1]. However, their work was not fully formal, par- tially because they used a semi-formal natural language to explain mathematical structuralism [1]. The invention of cat- egory theory in the forties provides a rigorous framework for structuring the mathematics [2]. It also provides an alterna- tive foundation for mathematics other than the set theory, in particular after the many setbacks the latter has suffered.Mathematics and structuralism Since a long time ago, scientists have pursued the idea of assigning each object of science with a structure. In the long run of history, this idea got a loud name of ＂structuralism＂ which received most attention from the mathematicians. The best known early work in ＂structural mathematics＂ was done by the Bourbaki School [1]. However, their work was not fully formal, par- tially because they used a semi-formal natural language to explain mathematical structuralism [1]. The invention of cat- egory theory in the forties provides a rigorous framework for structuring the mathematics [2]. It also provides an alterna- tive foundation for mathematics other than the set theory, in particular after the many setbacks the latter has suffered.

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程] F061.3[自动化与计算机技术—控制科学与工程]