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.
Theory and Applications of Categories25(17), 436–489 (2011) 2, 7
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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.