Topic: category theory

Investigate differential and tangent categories with Jean-Simon Pacaud Lemay in the School of Mathematical and Physical Sciences. The project connects category theory with differential or algebraic geometry and potential applications in computer science. This two-year, full-time research appointment has a flexible starting date in 2027. Annual pay is AUD 112,550–120,621 plus 17% superannuation and leave loading. International applications are welcome.

In this talk, I’ll introduce the formal concept of a (pre)sheaf as data attached to a topological space. Sheaves capture the notion of patching local sources of information to form a global whole, e.g., the binding of visual features such as colour and shape. The formal theory appears to be closely related to the foundational properties asserted by the Information Integration Theory (IIT) for phenomenology. A comparison is intended to engender discussion on ways that phenomenology may benefit from a sheaf theory, or (more generally) a category theory approach.

Category theory is a branch of mathematics which have been used to organize various regions of mathematics and related sciences from a radical “relation-first” point of view. Why consciousness researchers should care about category theory? " "There are (at least) 3 reasons:" "1 Everything is relational" "2 Everything is relation" "3 Relation is everything" "In this talk we explain the reasons above more concretely and introduce the ideas to utilize basic concepts in category theory for consciousness studies.