A lattice-theoretical perspective on adhesive categories

Paolo Baldan, Filippo Bonchi, Andrea Corradini, Tobias Heindel, Barbara König

Research output: Contribution to journalArticlepeer-review

Abstract

It is a known fact that the subobjects of an object in an adhesive category form a distributive lattice. Building on this observation, in the paper we show how the representation theorem for finite distributive lattices applies to subobject lattices. In particular, we introduce a notion of irreducible object in an adhesive category, and we prove that any finite object of an adhesive category can be obtained as the colimit of its irreducible subobjects. Furthermore we show that every arrow between finite objects in an adhesive category can be interpreted as a lattice homomorphism between subobject lattices and, conversely, we characterize those homomorphisms between subobject lattices which can be seen as arrows.
Original languageEnglish
Pages (from-to)222-245
Number of pages24
JournalJournal of Symbolic Computation
Volume46
Issue number3
DOIs
Publication statusPublished - Mar 2011

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