A 2-categorical approach to change of base and geometric morphisms. II.
A brief review of abelian categorifications.
A cartesian closed extension of a category of affine schemes
A categorical approach to integration.
A categorical concept of completion of objects
We introduce the concept of firm classes of morphisms as basis for the axiomatic study of completions of objects in arbitrary categories. Results on objects injective with respect to given morphism classes are included. In a finitely well-complete category, firm classes are precisely the coessential first factors of morphism factorization structures.
A categorical guide to separation, compactness and perfectness.
A category theoretical background for homomorphism theorems
A characterization of K-ary algebraic categories.
A characterization of locally -presentable categories
A classification of degree functors, I
A classification of degree functors, II
A coalgebraic view on reachability
Coalgebras for an endofunctor provide a category theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra...
A completion functor for Cauchy groups.
A concentration of categories with non-injective monomorphisms
A construction of -filtered bicolimits of categories
A construction of right groups from a connected groupoid.
A Continuity Criterion for Functors.
A convenient category for directed homotopy.
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.