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C. Conv and . .. Dill, 115 6.4.1.1 An internal hom-set on convenient sets, vol.117

.. .. Additive,

(. (f)-spaces and . .. Df)-spaces, 1.2 (F)-spaces and the ? product

. Nuclear and . .. Schwartz'-spaces,

. Kernel and . .. Distributions, 3.2 Distributions and distributions with compact support

. .. , 136 7.4.1 The categorical structure of Nuclear and (F)-spaces, Smooth Differential Linear Logic and its models

. .. Distributions, 144 7.5.3 Co-multiplication, and the bialgebraic natural transformations

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, 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

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?. Weake,

P. Especially, . E-:-p!-c-e, . Weake,-c-e-q-/-/-p!-c-!-c-e, and . Weak!-c-e,-c-!-c-e,

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, 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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