Constructs the exponential A^B and proves existence of tensor A ⊗ B on contextual categories such that bimorphisms correspond to morphisms from the tensor, extending to a closed symmetric monoidal structure on Cont.
Subsystems and regular quotients of C-systems
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abstract
C-systems were introduced by J. Cartmell under the name "contextual categories". In this note we study sub-objects and quotient-objects of C-systems. In the case of the sub-objects we consider all sub-objects while in the case of the quotient-objects only {\em regular} quotients that in particular have the property that the corresponding projection morphism is surjective both on objects and on morphisms. It is one of several short papers based on the material of the "Notes on Type Systems" by the same author. This version is essentially identical with the version published in Contemporary Mathematics n.658.
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2026 1verdicts
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A monoidal category of dependently sorted algebraic theories II: categorical aspects
Constructs the exponential A^B and proves existence of tensor A ⊗ B on contextual categories such that bimorphisms correspond to morphisms from the tensor, extending to a closed symmetric monoidal structure on Cont.