Integral Categories and Calculus Categories

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atmire.migration.oldid5516
dc.contributor.advisorBauer, Kristine
dc.contributor.advisorCockett, Robin
dc.contributor.authorLemay, Jean-Simon
dc.contributor.committeememberLaflamme, Claude
dc.contributor.committeememberBrenken, Berndt
dc.contributor.committeememberTasson, Christine
dc.date.accessioned2017-05-01T15:43:03Z
dc.date.available2017-05-01T15:43:03Z
dc.date.issued2017
dc.date.submitted2017en
dc.description.abstractDifferential categories are now a well-studied abstract setting for differentiation. However not much attention has been given to the process which is inverse to differentiation: integration. This thesis presents an analogous study of integral categories. Integral categories give an abstraction of integration by axiomatizing extra structure on a symmetric monoidal categories with a coalgebra modality using the primary rules of integration. The axioms for integrations include the analogues of integration by parts rule, also called the Rota-Baxter rule, the independence of the order of iterated integrals and that integral of any constant map is linear. We expect consequences of the compatible interaction between integration and differentiation to include the two fundamental theorems of calculus. A differential category with integration which satisfies these two theorem in a suitable sense is what we call a calculus category.en_US
dc.identifier.citationLemay, J. (2017). Integral Categories and Calculus Categories (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26565en_US
dc.identifier.doihttp://dx.doi.org/10.11575/PRISM/26565
dc.identifier.urihttp://hdl.handle.net/11023/3764
dc.language.isoeng
dc.publisher.facultyGraduate Studies
dc.publisher.institutionUniversity of Calgaryen
dc.publisher.placeCalgaryen
dc.rightsUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.
dc.subjectMathematics
dc.subject.otherDifferential Categories
dc.subject.otherIntegral Categories
dc.subject.otherCalculus Categories
dc.subject.otherFundamental Theorems of Calculus
dc.subject.otherLinear Logic
dc.subject.otherCategory Theory
dc.subject.otherCalculus
dc.titleIntegral Categories and Calculus Categories
dc.typemaster thesis
thesis.degree.disciplineMathematics and Statistics
thesis.degree.grantorUniversity of Calgary
thesis.degree.nameMaster of Science (MSc)
ucalgary.item.requestcopytrue
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