does category theory subsume type theory

Introduction: The Systematicity Challenge If context is a category, then a natural extension toward addressing this question is higher-order category theory, where categories themselves are the objects of construction.ġ. The ultimate challenge, then, is to explain the determination of context.

From this view, universal constructions are derived from learning, as an optimization. Moreover, every universal construction can be viewed as the optimal construction in the given context (category). As a mathematical theory of structure, category theory provides necessary and sufficient conditions for systematicity in the form of universal construction: each systematically related cognitive capacity is composed of a common component and a unique component. We review an alternative, category theory approach to the systematicity problem. Hence, these approaches fail to fully explain why systematicity is a (near) universal property of human cognition, albeit in restricted contexts. That is, their core principles and assumptions do not provide the necessary and sufficient conditions from which systematicity follows, as required of a causal theory. However, the predominant theoretical approaches to the systematicity problem, i.e., classical (symbolic) and connectionist (subsymbolic), require arbitrary ( ad hoc) assumptions to derive systematicity. Systematicity is generally considered to involve a capacity to represent/process common structural relations among the equivalently cognizable entities. Why does the capacity to think certain thoughts imply the capacity to think certain other, structurally related, thoughts? Despite decades of intensive debate, cognitive scientists have yet to reach a consensus on an explanation for this property of cognitive architecture-the basic processes and modes of composition that together afford cognitive capacity-called systematicity. 2School of Computer Science and Engineering, University of New South Wales, Sydney, NSW, Australia.1Mathematical Neuroinformatics Group, Human Informatics Research Institute, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan.

Does category theory subsume type theory