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Showing 1 to 9 of 9 for “"cartesian closed"”.
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Cartesian closed bicategories: type theory and coherence
… between the simply-typed lambda calculus and cartesian closed categories to the bicategorical setting, then use the resulting type theory to prove a coherence result for cartesian closed bicategories. Cartesian closed bicategories---2-categories `up to isomorphism' equipped with similarly weak …
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Internal monoid actions in a cartesian closed category and higher-dimensional group automorphisms
… n-fold categories in the category of groups is a cartesian closed category, however given an object X in Catⁿ (Groups), calculating corresponding action representing object Aut (X) directly would require an enormous calculations. The main purpose of the thesis is to describe that object avoiding …
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A Wyler-type approach to categorical topology
… property with respect to pullbacks. The cartesian closed topological categories are characterised as those categories of T-models where the associated theory T sends a pointwise pullback of any regular sink into product covering family of diagrams. The concretely cartesian closed …
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A theory of elementary higher toposes
… spaces and use that to define representable Cartesian fibrations. Next we use representable Cartesian fibrations to define complete Segal objects which are are model for internal higher categories. Having done all this work we can then define an elementary higher topos which simultaneously …
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Problems in the Theory of Convergence Spaces
… theory; we then generalize these results to the cartesian closed category of convergence spaces. Finally, we show that every convergence space can be embedded into a homogeneous convergence space; we then use this result to construct a universal homogeneous pretopological space.</p>
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Polynomials and models of type theory
… that although the base category is not locally cartesian closed, this model has dependent product types. Finally, we investigate the properties of identity types in this model, and consider the link with functional interpretations in logic.
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Categories with New Foundations
… justification. The category of NF sets is not cartesian closed and the failure of choice is a theorem of NF. But those results should not obscure the aspects of NF that have foundational appeal, nor the value of studying category theory in the context of a universal set. The present research is …
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Probabilistic concurrent game semantics
… We show that they form a symmetric monoidal closed bicategory, and that this can be turned into a cartesian closed bicategory using a linear exponential pseudo-comonad inspired by linear logic. Then, we enrich this with probability, relying heavily on Winskel's model of probabilistic …
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A CATEGORICAL-ALGEBRAIC EXPLORATION OF MODELS FOR MANY-VALUED LOGIC
… namely it is fiber-wise algebraically cartesian closed, strongly protomodular, and its full subcategory of lattice-ordered abelian groups is algebraically coherent. In the second part, we observe that the category of MV-algebras is protomodular and arithmetical, and we pursue a thorough …