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math.CT2023
Left adjoint to precomposition in elementary doctrines
Francesca Guffanti
It is well-known in universal algebra that adding structure and equational axioms generates forgetful functors between varieties, and such functors all have left adjoints. The cate…
math.CT2023
Rich doctrines and Henkin's Theorem
Francesca Guffanti
We find a possible interpretation of Henkin's Theorem in the language of existential implicational doctrines. Under some smallness assumption, starting from an implicational existe…
math.CT2023
Adding a constant and an axiom to a doctrine
Francesca Guffanti
We study the meaning of "adding a constant to a language" for any doctrine, and "adding an axiom to a theory" for a primary doctrine, by showing how these are actually two instance…