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115 6.4.1.1 An internal hom-set on convenient sets, vol.117 ,
,
1.2 (F)-spaces and the ? product ,
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3.2 Distributions and distributions with compact support ,
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144 7.5.3 Co-multiplication, and the bialgebraic natural transformations ,
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the full subcategory of spaces having their Mackey topology. µSch ? LCS the full subcategory of spaces having the Schwartz topology associated to its Mackey topology ,
, And then by intersection always considered as full subcategories, one obtains: and by the universal property this gives S pEq » ' iPI S pE i q. Therefore, if all spaces E i are ?-reflexive, E carries the Schwartz topology associated to its Mackey topology, Mb ? LCS the full subcategory of spaces with a Mackey-complete Mackey dual
,
,
,
q making WEAKE, c E coalgebra morphisms. For instance, µ 0 : R / / ! C pRq (the space of distributions) is given by ,
, the setting of Theorem B.2.18, and we will use it in this setting later. As explained in [25], the only missing piece of structure to get a bicomoid structure on every ! C E is a biproduct compatible with the symmetric monoidal structure, or equivalently a Mon-enriched symmetric monoidal category, where Mon is the category of monoids
, A general construction for DiLL models We define N L C pU pEqq as the limit in C of Dif f E . Note that, since`C commutes with limits in C, N L C pU pEqq
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