Topoi: The Categorial Analysis of Logic

Aclassicintroductiontomathematicallogicfromtheperspectiveofcategorytheory,thistextissuitableforadvancedundergraduatesandgraduatestudentsandaccessibletobothphilosophicallyandmathematicallyorientedreaders.Itsapproachmovesalwaysfromtheparticulartothegeneral,followingthroughthestepsoftheabstractionprocessuntiltheabstractconceptemergesnaturally.Beginningwithasurveyofsettheoryanditsroleinmathematics,thetextproceedstodefinitionsandexamplesofcategoriesandexplainstheuseofarrowsinplaceofset-membership.Theintroductiontotoposstructurecoverstoposlogic,algebraofsubobjects,andintuitionismanditslogic,advancingtotheconceptoffunctors,setconceptsandvalidity,andelementarytruth.Explorationsofcategorialsettheory,localtruth,andadjointnessandquantifiersconcludewithastudyoflogicalgeometry.