Cartesian Closed Categories and Typed Lambda Calculi

dc.contributor.advisorBlumberg, Andrew
dc.creatorMenezes, Dean
dc.date.accessioned2023-09-25T12:12:55Z
dc.date.available2023-09-25T12:12:55Z
dc.date.issued2016
dc.description.abstractTyped lambda categories and Cartesian closed categories are both means of formalizing the process of substitution; we demonstrate that these views are essentially the same; specifically that there is an equivalence between the category of small Cartesian closed categories and the category of typed lambda calculi. First we introduce the basic notions of category, functor, monad, comonad and equivalence of categories; then we use these notions to define the category of small Cartesian closed categories and describe how additional arrows may be adjoined to a Cartesian closed category. Next we provide a definition of a typed lambda calculus and describe the structure-preserving maps or translations between typed lambda calculi. Next we provide a definition of a typed lambda calculus and describe the structure-preserving maps or translations between typed lambda calculi. Having defined the two categories we provide descriptions of functors L : Cart_N to lambda-calc and C: lambda-calc to Cart_N and then show that the functors give an equivalence of categories.en_US
dc.description.departmentMathematicsen_US
dc.identifier.urihttps://hdl.handle.net/2152/121783
dc.identifier.urihttp://dx.doi.org/10.26153/tsw/48609
dc.language.isoengen_US
dc.relation.ispartofHonors Thesesen_US
dc.rights.restrictionOpenen_US
dc.subjecttyped lambda categoriesen_US
dc.subjectCartesian closed categoriesen_US
dc.subjectequivalenceen_US
dc.subjectcategoryen_US
dc.subjectfunctoren_US
dc.subjectmonaden_US
dc.subjectcomonaden_US
dc.subjectmathen_US
dc.subjectlogicen_US
dc.subjectcategory theoryen_US
dc.titleCartesian Closed Categories and Typed Lambda Calculien_US
dc.typeThesisen_US

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