Projective Covers of 2-star-permutable Categories
Vasileios Aravantinos-Sotiropoulos
TL;DR
This paper introduces star-symmetry in multi-pointed categories to characterize projective covers of 2-star-permutable categories, generalizing previous results and connecting to E-subtractive varieties.
Contribution
It defines star-symmetry and uses it to characterize projective covers in 2-star-permutable categories, extending prior work on Mal'tsev and subtractive categories.
Findings
Characterization of projective covers via star-symmetry
Generalization of Mal'tsev and subtractive categories results
Recovery of E-subtractive variety conditions
Abstract
We introduce the notion of star-symmetry for relations in a multi-pointed category and use it to obtain a characterization of the projective covers of 2-star-permutable categories. This generalizes the results of Rosick\'y-Vitale for regular Mal'tsev categories, as well as those of Gran-Rodelo for regular subtractive categories. We apply the characterization in terms of star-symmetry to recover the syntactic conditions defining E-subtractive varieties in the sense of Ursini.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra