-homotopy theory of schemes
A -categorical approach to change of base and geometric morphisms I
A 2-categorical approach to change of base and geometric morphisms. II.
A bicategorical approach to static modules.
A Borel topos
A brief review of abelian categorifications.
A cartesian closed extension of a category of affine schemes
A categorical account of the localic closed subgroup theorem
Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
A categorical approach to integration.
A categorical approach to invariant means and fixed point properties.
A categorical characterization of sets among classes
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 genealogy for the congruence distributive property.
A categorical generalization of a theorem of G. Birkhoff on primitive classes of universal algebras
A categorical guide to separation, compactness and perfectness.
A categorical view at generalized concept lattices
We continue in the direction of the ideas from the Zhang’s paper [Z] about a relationship between Chu spaces and Formal Concept Analysis. We modify this categorical point of view at a classical concept lattice to a generalized concept lattice (in the sense of Krajči [K1]): We define generalized Chu spaces and show that they together with (a special type of) their morphisms form a category. Moreover we define corresponding modifications of the image / inverse image operator and show their commutativity...
A categorification of the square root of -1
We give a graphical calculus for a monoidal DG category ℐ whose Grothendieck group is isomorphic to the ring ℤ[√(-1)]. We construct a categorical action of ℐ which lifts the action of ℤ[√(-1)] on ℤ².
A category model proof of the cogluing theorem
A category theoretical background for homomorphism theorems
A characterization of a category of discrete transformation groups