-Cat is locally presentable or locally bounded if is so.
-purity and orthogonality.
-semiring pairs
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.
A characterization of K-ary algebraic categories.
A characterization of locally -presentable categories
A characterization of varieties of inverse semigroups.
A coalgebraic semantics of subtyping
Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.
A Coalgebraic Semantics of Subtyping
Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.
A convenient category for directed homotopy.
A counterexample to a conjecture of Barr.
A duality between infinitary varieties and algebraic theories
A duality between -ary varieties and -ary algebraic theories is proved as a direct generalization of the finitary case studied by the first author, F.W. Lawvere and J. Rosick’y. We also prove that for every uncountable cardinal , whenever -small products commute with -colimits in , then must be a -filtered category. We nevertheless introduce the concept of -sifted colimits so that morphisms between -ary varieties (defined to be -ary, regular right adjoints) are precisely the functors...
A duality relative to a limit doctrine.
A functional representation of the hyperspace monad
A functional representation of the hyperspace monad, based on the semilattice structure of function space, is constructed.
A generalized global differential calculus : application to invariance under a Lie group. I
A logic of injectivity.
A logic of orthogonality
A logic of orthogonality characterizes all “orthogonality consequences" of a given class of morphisms, i.e. those morphisms such that every object orthogonal to is also orthogonal to . A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes of morphisms such that all members except a set are regular epimorphisms and (b) for all classes , without...
A monadic approach to polycategories.
A new proof of Reiterman's theorem
A note on actions of a monoidal category.
A note on algebraic categories