Applicable categorical structures

点击翻译按钮获取中文摘要

Mathematical research, like other endeavours, operates in specified environments: a space of numbers or vectors, a category of sets perhaps with extra structure, or a category of spaces. Often the environment is a specific category and analysis is internal to that. The novelty of category theory is that it applies also to external relations among the various environments. The direction of our work is motivated by aspects of mathematics, theoretical physics, and computer science. Such work underpins the capacity of the private sector by providing skilled graduates and enhancing the capabilities of the economy. Australia must maintain expertise in basic science and technology to be ready for uncertain future demands.