Category of commutative groupoids is binding
Cauchy-completion and the associated sheaf
CCD lattices in presheaf categories.
Čech extensions and localization of homotopy functors
Čech-Stone-like compactifications for general topological spaces
The problem whether every topological space has a compactification such that every continuous mapping from into a compact space has a continuous extension from into is answered in the negative. For some spaces such compactifications exist.
Central extensions and reciprocity laws
Centrality and normality in protomodular categories.
Change of base for relational variable sets.
Characterization of fuzzy order relation by fuzzy cone
In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed...
Characterizations of Lambek-Carlitz type
We give Lambek-Carlitz type characterization for completely multiplicative reduced incidence functions in Möbius categories of full binomial type. The -analog of the Lambek-Carlitz type characterization of exponential series is also established.
Charakterisierung nüchterner Räume.
Classification of concrete geometrical categories.
Classification of tensor products of symmetric graphs
In the category of symmetric graphs there are exactly five closed tensor products. If we omit the requirement of units, we obtain twelve more.
Closure operators in exact completions.
Closure operators on O-categories.
Coarse dimensions and partitions of unity.
Gromov and Dranishnikov introduced asymptotic and coarse dimensions of proper metric spaces via quite different ways. We define coarse and asymptotic dimension of all metric spaces in a unified manner and we investigate relationships between them generalizing results of Dranishnikov and Dranishnikov-Keesling-Uspienskij.
Coarse structures and group actions
The main results of the paper are: Proposition 0.1. A group G acting coarsely on a coarse space (X,𝓒) induces a coarse equivalence g ↦ g·x₀ from G to X for any x₀ ∈ X. Theorem 0.2. Two coarse structures 𝓒₁ and 𝓒₂ on the same set X are equivalent if the following conditions are satisfied: (1) Bounded sets in 𝓒₁ are identical with bounded sets in 𝓒₂. (2) There is a coarse action ϕ₁ of a group G₁ on (X,𝓒₁) and a coarse action ϕ₂ of a...
Codensity and binding categories
Coequalizers in the generalized algebraic categories
Cofibrations and the realization of non-deterministic automata