Applicable categorical structures

数学研究，像其他努力一样，在特定的环境中进行：一个数字或向量的空间，一个可能具有额外结构的集合的范畴，或者一个空间的范畴。通常情况下，环境是一个特定的类别，而分析是内部的。范畴论的新颖之处在于它也适用于各种环境之间的外部关系。我们的工作方向是由数学、理论物理和计算机科学的各个方面驱动的。这些工作通过提供熟练的毕业生和增强经济能力，巩固了私营部门的能力。澳大利亚必须保持在基础科学和技术方面的专门知识，以便为不确定的未来需求做好准备。

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.