Symmetry, Geometry, Modality.

dc.contributor.advisorRiehl, Emily
dc.contributor.advisorRynasiewicz, Robert
dc.contributor.committeeMemberBaez, John C
dc.contributor.committeeMemberKitchloo, Nitu
dc.contributor.committeeMemberGepner, David
dc.creatorMyers, David Jaz
dc.creator.orcid0000-0002-4237-0611
dc.date.accessioned2022-09-26T19:09:40Z
dc.date.available2022-09-26T19:09:40Z
dc.date.created2022-08
dc.date.issued2022-07-12
dc.date.submittedAugust 2022
dc.date.updated2022-09-26T19:09:40Z
dc.description.abstractThis thesis consists of four studies into symmetry and geometry in modal homotopy type theory. First, we prove a higher analogue of Schreier's classificiation of group extensions by means of non-abelian cohomology. Second, we put forward a definition of modal fibration suitable for synthetic algebraic topology, and characterize the modal fibrations for the homotopy type modality as those maps for which the homotopy types of their fibers form a local system on the homotopy type of the base. Third, we put forward a synthetic definition of orbifold, and show that all proper \'etale groupoids are orbifolds in this sense. And fourth, we construct the modal fracture hexagon of a higher group, and use this to derive the differential cohomology hexagon in synthetic differential geometry.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://jhir.library.jhu.edu/handle/1774.2/67618
dc.language.isoen_US
dc.publisherJohns Hopkins University
dc.publisher.countryUSA
dc.subjectModality
dc.subjectHomotopy Type Theory
dc.subjectSynthetic Differential Geometry
dc.subjectCategory Theory
dc.titleSymmetry, Geometry, Modality.
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorJohns Hopkins University
thesis.degree.grantorKrieger School of Arts and Sciences
thesis.degree.levelDoctoral
thesis.degree.namePh.D.
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