منابع مشابه
Modular correspondence between dependent type theories and categories including pretopoi and topoi
We present a modular correspondence between various categorical structures and their internal languages in terms of extensional dependent type theories à la Martin-Löf. Starting from lex categories, through regular ones we provide internal languages of pretopoi and topoi and some variations of them, like for example Heyting pretopoi. With respect to the internal languages already known for some...
متن کاملSheaf representation for topoi
It is shown that every (small) topos is equivalent to the category of global sections of a sheaf of so-called hyperlocal topoi, improving on a result of Lambek & Moerdijk. It follows that every boolean topos is equivalent to the global sections of a sheaf of well-pointed topoi. Completeness theorems for higher-order logic result as corollaries. The main result of this paper is the following. Th...
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The term “Boolean category” should be used for describing an object that is to categories what a Boolean algebra is to posets. More specifically, a Boolean category should provide the abstract algebraic structure underlying the proofs in Boolean Logic, in the same sense as a Cartesian closed category captures the proofs in intuitionistic logic and a *-autonomous category captures the proofs in ...
متن کاملOn the Axiomatisation of Boolean Categories with and without Medial
In its most general meaning, a Boolean category is to categories what a Boolean algebra is to posets. In a more specific meaning a Boolean category should provide the abstract algebraic structure underlying the proofs in Boolean Logic, in the same sense as a Cartesian closed category captures the proofs in intuitionistic logic and a *-autonomous category captures the proofs in linear logic. How...
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This paper studies numerals (see definition that immediately follows), natural numbers objects and, more generally, free actions, in a topos. A pre-numeral is a poset with a constant, 0, and a unary operation, s, such that: PN1) x ≤ y ⇒ sx ≤ sy PN2) x ≤ sx A numeral is a “minimal” pre-numeral, that is, one such that any s-invariant subobject containing 0 is entire. 1. Lemma. A pre-numeral is a ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1973
ISSN: 0022-4049
DOI: 10.1016/0022-4049(73)90009-1