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The notion of a natural numbers object in a monoidal category is defined and it is shown that the theory of primitive recursive functions can be developed. This is done by considering the category of cocommutative comonoids which is cartesian, and where the theory of natural numbers objects is well developed. A number of examples illustrate the usefulness… (More)
We present an internal language for symmetric monoidal closed (autonomous) categories analogous to the typed lambda calculus as an internal language for cartesian closed categories. The language we propose is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous… (More)
Let L be an arbitrary orthomodular lattice. There is a one to one correspondence between orthomodular sublattices of L satisfying an extra condition and quantic quantifiers. The category of orthomodular lattices is equivalent to the category of posets having two families of endofunctors satisfying six conditions.
Let L be a complete orthomodular lattice. There is a one to one correspondence between complete boolean subalgebras of L contained in the center of L and endomorphisms j of L satisfying the Borceux-Van den Bossche conditions.