* Nomenclature question
@ 2019-05-04 0:17 David Roberts
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From: David Roberts @ 2019-05-04 0:17 UTC (permalink / raw)
To: categories@mta.ca list
Hello all,
is there a name in the literature for a category C equipped with a
product functor
#: C x C ---> C
satisfying *no* axioms? This is a magma object in Cat, but calling
'magma category' seems at risk of confusion. A name that occurred to
me is 'magmoidal category', as a portmanteau of 'magma' and 'monoidal
category'.
Such a category can be further equipped with diagonals, hence a
natural transformation id_C => # \Delta_C, for \Delta_C: C --> C x C.
Magmoidal categories with diagonals cropped up as a natural minimal
requirements for a particular proof, but it's far from clear that
nontrivial and non-degenerate examples exist.
David
David Roberts
Webpage: https://ncatlab.org/nlab/show/David+Roberts
Blog: https://thehighergeometer.wordpress.com
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