Year: 2024
Type: article
Abstract: Suppose $$(\mathcal {C},\mathbb {E},\mathfrak {s})$$ ( C , E , s ) is an n-exangulated category. We show that the idempotent completion and the weak idempotent completion of $$\mathcal {C}$$ C are again n-exangulated categories. Furthermore, we also show that the canonical inclusion functor of $$\mathcal {C}$$ C into its (resp. weak) idempotent completion is n-exangulated and 2-universal among n-exangulated functors from $$(\mathcal {C},\mathbb {E},\mathfrak {s})$$ ( C , E , s ) to (resp. weakly) idempotent complete n-exangulated categories. Furthermore, we prove that if $$(\mathcal {C},\mathbb {E},\mathfrak {s})$$ ( C , E , s ) is n-exact, then so too is its (resp. weak) idempotent completion. We note that our methods of proof differ substantially from the extriangulated and $$(n+2)$$ ( n + 2 ) -angulated cases. However, our constructions recover the known structures in the established cases up to n-exangulated isomorphism of n-exangulated categories.
Source: Applied Categorical Structures
Authors: Carlo Klapproth, Dixy Msapato, Amit Shah
Institutions: Aarhus University, University of Leeds
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4391657473