Lax naturality through enrichment

Yoshiki Kinoshita and John Power

Abstract: We develop the relationship between algebraic structure and monads enriched over the monoidal biclosed category LocOrdi of small locally ordered categories, with closed structure given by Lax(A,B). We state the theorem, give a series of examples, and incorporate an account of sketches and contravariance into the theory. This was motivated by C.A.R. Hoare's use of category theoretic structures to model data refinement.

ECS-LFCS-95-330, August 1995.

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