Seven Sketches in Compositionality：An Invitation to Applied Category Theory

Categorytheoryisunmatchedinitsabilitytoorganizeandlayerabstractionsandtofindcommonalitiesbetweenstructuresofallsorts.Nolongertheexclusivepreserveofpuremathematicians,itisnowprovingitselftobeapowerfultoolinscience,informatics,andindustry.Byfacilitatingcommunicationbetweencommunitiesandbuildingrigorousbridgesbetweendisparateworlds,appliedcategorytheoryhasthepotentialtobeamajororganizingforce.Thisbookoffersaself-containedtourofappliedcategorytheory.Eachchapterfollowsasinglethreadmotivatedbyareal-worldapplicationanddiscussedwithcategory-theoretictools.Weseedatamigrationasanadjointfunctor,electricalcircuitsintermsofmonoidalcategoriesandoperads,andcollaborativedesignviaenrichedprofunctors.Alltherelevantcategorytheory,fromsimpletosophisticated,isintroducedinanaccessiblewaywithmanyexamplesandexercises,makingthisanidealguideevenforthosewithoutexperienceofuniversity-levelmathematics.