Instances of models of double theories are defined as presheaves on lax double functors and shown equivalent to modules from the terminal model or loose natural transformations, with an elements correspondence to discrete opfibrations.
S., P ATTERSON , E., AND SHAPIRO , B
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Introduces sheaf-theoretic categories of narratives on time-interval posets as a general framework for time-varying data that satisfies five desiderata from temporal graph theory and generalizes to any category with limits and colimits.
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Presheaves on lax double functors; or, Instances of models of double theories
Instances of models of double theories are defined as presheaves on lax double functors and shown equivalent to modules from the terminal model or loose natural transformations, with an elements correspondence to discrete opfibrations.
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Towards a Unified Theory of Time-Varying Data
Introduces sheaf-theoretic categories of narratives on time-interval posets as a general framework for time-varying data that satisfies five desiderata from temporal graph theory and generalizes to any category with limits and colimits.