Parallelism Theorem and Derived Rules for Parallel Coherent Transformations

Abstract : An Independent Parallelism Theorem is proven in the theory of adhesive HLR categories. It shows the bijective correspondence between sequential independent and parallel independent direct derivations in the Weak Double-Pushout framework, see [2]. The parallel derivations are expressed by means of Parallel Coherent Transformations (PCTs), hence without assuming the existence of coproducts compatible with M as in the standard Parallelism Theorem. It is aslo shown that a derived rule can be extracted from any PCT, in the sense that to any direct derivation of this rule corresponds a valid PCT.
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http://hal.univ-grenoble-alpes.fr/hal-02325194
Contributor : Thierry Boy de la Tour <>
Submitted on : Tuesday, October 22, 2019 - 10:58:04 AM
Last modification on : Friday, October 25, 2019 - 1:27:43 AM

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  • HAL Id : hal-02325194, version 1
  • ARXIV : 1907.06585

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Thierry Boy de la Tour, Thierry Boy de la Tour. Parallelism Theorem and Derived Rules for Parallel Coherent Transformations. 2019. ⟨hal-02325194⟩

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