Content pages

For long-form content and reusable lemmas, we use content pages.

• A classification of congruences in the category of sets and relations
• Algebraic categories are "never" thin
• An embedding of the category of topological spaces in the category of locally ringed spaces
• Cocongruences in extensive categories
• Cocongruences of groups are effective
• Cogenerators in product categories
• Construction of a pushout of monomorphisms as a quotient of a congruence
• Construction of generators
• Cototal algebraic categories
• Dual properties
• Explicit proof that the category of groups is total
• Extremal generators in thin categories
• Finite structures usually have no sequential colimits
• Finitely generated groups are not closed under ℵ₁-cofiltered limits
• Finitely generated groups do not have ℵ₁-filtered colimits
• Foundations
• Functors on discrete categories
• How to contribute to CatDat
• Inclusion functors
• Infinite products and coproducts in additive categories
• Inheritance of effective congruences in coslice categories
• Isbell's condition for concretizability
• Local ℵ₁-copresentability of the category of compact Hausdorff spaces
• Missing cogenerating collections
• Missing cogenerator
• Natural numbers objects
• Nice and small presheaves
• Pushouts of uniform embeddings
• Quotients of effective congruences
• Regular epimorphisms are coequalizers of their kernel pairs
• Relationships between epimorphisms and monomorphisms
• Resources on category theory
• Results on constant morphisms
• Results on subcategories
• Sifted colimits in groupoids
• The colimit of a sequence of monomorphisms
• The free cocompletion of a locally small category
• Topos with a generator
• Uniqueness of preadditive structures