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math.CT2026
Quantification in Double-Categorical Database Schemas
Michael Lambert
Double-categorical database schemas are enriched with universal quantification in the form of right adjoints to substitution. This allows phrasing of the important query, relationa…
math.CT2026
Twisted double functors and loosely discrete opfibrations
Michael Lambert, David Jaz Myers, Evan Patterson
Various situations in the theory and applications of double categories, ranging from a loose Yoneda theory and loose compact closure to double-operadic systems theory, require a no…
math.CT2025
Representing Knowledge and Querying Data using Double-Functorial Semantics
Michael Lambert, Evan Patterson
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the cate…