Enrichment Through Variation

R. Gordon and A. J. Power

Abstract: We show that, for a closed bicategory W, the 2-category of tensored W-categories and all W-functors between them is equivalent to the 2-category of closed W- representations and maps of such, which in turn is isomorphic to a full sub-2-category of Lax(W, Cat). We further show that, if w is a locally dense subbicategory of W and W is biclosed, then the 2-category of W-categories having tensors with 1-cells of w embeds fully into the 2-category of w-representations. This allows us to generalize Gabriel-Ulmer duality to W-categories and to prove, for W-categories, that for locally finitely presentable A and for B admitting finite tensors and filtered colimits, the category of W-functors from Af to B is equivalent to that of finitary W-functors from A to B.

LFCS report ECS-LFCS-93-254

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