Towards Secrecy for Rewriting in Weakly Adhesive Categories

Heindel, Tobias

doi:10.1016/j.entcs.2009.06.041

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Finite Objects As Vk-colimits Of Irreducibles1

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2011

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“…All vertical squares are known to be pullbacks, except for the rightmost square in the display above. However, reusing the proof idea of Proposition 4.4 of (Heindel, 2009), also this square can be shown to be a pullback. For arrows y ⊑ x in I, the relevant naturality square can similarly be shown to be a pullback, this time using the pushouts based on the I-objects z ⊓ y, u ⊓ y, v ⊓ y, y.…”

Section: Finite Objects As Vk-colimits Of Irreduciblesmentioning

confidence: 94%

A lattice-theoretical perspective on adhesive categories

Baldan

Bonchi

Corradini

et al. 2011

Journal of Symbolic Computation

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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

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Section: Finite Objects As Vk-colimits Of Irreduciblesmentioning

confidence: 94%