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![Figure 1: [CD.5] in XS, continued in Figure 2](https://thumb-ap.123doks.com/thumbv2/123dok/924079.902872/28.612.76.534.102.685/figure-cd-in-xs-continued-in-figure.webp)
![Figure 2: [CD.5] in XS, continued from Figure 1](https://thumb-ap.123doks.com/thumbv2/123dok/924079.902872/29.612.76.526.88.689/figure-cd-in-xs-continued-from-figure.webp)
![Figure 3: (1 × π)D×[f] in X](https://thumb-ap.123doks.com/thumbv2/123dok/924079.902872/30.612.73.529.322.644/figure-p-d-f-in-x.webp)
![Figure 5: (⟨1, 0⟩ × 1)D×[D×[f]] in X](https://thumb-ap.123doks.com/thumbv2/123dok/924079.902872/31.612.77.525.211.576/figure-d-d-f-in-x.webp)
![Figure 7: ⟨⟨0, h⟩, ⟨g, k⟩⟩D×[D×[f]]](https://thumb-ap.123doks.com/thumbv2/123dok/924079.902872/33.612.72.526.160.623/figure-h-g-k-d-d-f.webp)
![Figure 8: ⟨⟨0, g⟩, ⟨h, k⟩⟩D×[D×[f]]](https://thumb-ap.123doks.com/thumbv2/123dok/924079.902872/34.612.73.529.246.528/figure-g-h-k-d-d-f.webp)
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Before treating the general case of enriching over the k -fold monoidal category of enriched n -categories we examine the definition in the two lowest categorical dimensions.. This
Namely, new factorization systems are constructed on the categories of Abelian groups (more generally, on any Abelian category), groups with unary operators, locally com- pact
We call them the left double , right double and double of the monoidal.. V
Here we consider a category of M¨obius intervals and construct the Hopf algebra via the objective approach applied to a monoidal extensive category of combinatorial objects, with
The proof of May's uniqueness theorem (Ma4] Thm. 3) for functors dened from the category of permutative categories easily generalizes to show any two functors from SymMon to
For any topos over sets a certain left exact cosimplicial category is constructed functorially and the cat- egory of internal categories in it is investigated.. The notion of
What Koslowski actually proves is that if you begin with a biclosed monoidal category there is a biclosed monoidal bicategory whose objects are the algebra objects in the
A Gray-monoid [DS97, Section 1] may be considered to be a monoidal2-category, and in fact every monoidal 2-category is biequivalent to a Gray-monoid [GPS95, Section 8.1]; indeed this
