Foundations of higher dimensional homological algebra

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Recent discoveries in physics and mathematics led to the understanding that classical mathematics is only 'the tip of the iceberg' of the higher-dimensional structures that are ultimately behind the laws of Nature. Australia has always been in the forefront of research in Category Theory, and due to that position, has a unique opportunity to participate in the early stages of developments of Higher Category Theory and Higher Dimensional Homological Algebra. This will allow Australia to be in the forefront of the subsequent technological development and to reap the economical, social and intellectual benefits related to it.