A category is subtractive if it is pointed, admits finite limits, and left punctual reflexive relations are right punctual.
Here a relation is left (respectively right) punctual if (respectively ) factors through .
A variety of algebras is a subtractive category if and only it is a subtractive variety in the sense of Ursini, meaning its theory contains a binary operation and constant such that and .
A category with finite limits is a Malcev category if and only if for any object of the category is subtractive.
Here is the pointed category whose objects are triples such that . Morphisms are morphisms such that and .
Zurab Janelidze, Subtractive categories, Appl. Categ. Struct 13, No. 4, 343-350 (2005) (doi:10.1007/s10485-005-0934-8)
Zurab Janelidze, Closedness properties of internal relations. A series of papers.
I. A unified approach to Malʹtsev, unital and subtractive categories.
II. Bourn localization.
III. Pointed protomodular categories.
IV. Expressing additivity of a category via subtractivity.
V. Linear Malʹtsev conditions.
VI. Approximate operations.
Last revised on October 12, 2022 at 09:53:40. See the history of this page for a list of all contributions to it.