What underlies dual-process cognition? Adjoint and representable functors

AbstractDespite a general recognition that there are two styles of thinking: fast, reflexive and relatively effortless (Type~1) versus slow, reflective and effortful (Type~2), dual-process theories of cognition remain controversial, in particular, for their vagueness. To address this lack of formal precision, we take a mathematical category theory approach towards understanding what underlies the relationship between dual cognitive processes. From our category theory perspective, we show that distinguishing features of Type~1 versus Type~2 processes are exhibited via adjoint and representable functors. These results suggest that category theory provides a useful formal framework for developing dual-process theories of cognition.

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