CatDat

epi-regular

A category is epi-regular when every epimorphism is regular, i.e. the coequalizer of a pair of morphisms. Notice that this is not standard terminology, apparently the literature has no name for this yet. A preadditive category is epi-regular iff every epimorphism is a cokernel, and this type of category is commonly known as a conormal category. We avoid this terminology here since it only applies to a certain type of categories, but epi-regular applies to all categories.

Relevant implications

Examples

Counterexamples

Unknown

For these categories the database has no info if they satisfy this property or not.