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SUMMARY:Amar Hadzihasanovic (Tallinn University of Technology)
DTSTART:20210520T133000Z
DTEND:20210520T143000Z
DTSTAMP:20260423T021237Z
UID:itaca/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/itaca/4/">Th
 e smash product of monoidal theories</a>\nby Amar Hadzihasanovic (Tallinn 
 University of Technology) as part of ItaCa Fest 2021\n\n\nAbstract\nThe sm
 ash product of pointed spaces is a classical construction of topology. The
  tensor product of props\, which extends both the Boardman-Vogt product of
  symmetric operads and the tensor product of Lawvere theories\, seems firm
 ly like a piece of universal algebra. \n\n In this talk\, we will see that
  the two are facets of the same construction: a “smash product of pointe
 d directed spaces”. Here\, “directed spaces” are modelled by combina
 torial structures called diagrammatic sets\, developed as a homotopically 
 sound foundation for diagrammatic rewriting in higher dimensions\, while t
 he cartesian product of spaces is replaced by a form of Gray product.\n Mo
 st interestingly\, the smash product applies to presentations of higher-di
 mensional theories and systematically produces oriented equations and high
 er-dimensional coherence data (oriented syzygies). This introduces a synth
 etic\, compositional method in rewriting on higher structures.\n \n\nThis 
 talk is based on my preprint arXiv:2101.10361 with the same title.\n
LOCATION:https://researchseminars.org/talk/itaca/4/
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