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![Table 2: k-alternating subsets of [m] of cardinality ≤ 3, for m ≥ 1](https://thumb-ap.123doks.com/thumbv2/123dok/917492.901520/44.595.140.463.631.692/table-k-alternating-subsets-m-cardinality-m.webp)
![Figure 9: (a) Element of A[1], with, for instance, the {0}-face labelled a0; (b) element ofA[2]; (c) (admissible) horn Λ12✲ A; (d) admissible horn Λ02✲ A, with ∼ indicatinga hollow face; (e) admissible horn Λ03✲ A, with labels fij, αijk omitted; (f) as (e), butfor Λ13.](https://thumb-ap.123doks.com/thumbv2/123dok/917492.901520/45.595.86.517.95.198/figure-element-instance-labelled-admissible-admissible-indicatinga-admissible.webp)
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Note that because the morphisms in Wk -2- Cat are strict maps (as noted on page 153), we obtain an equivalence with UBicat str, not UBicat wk or UBicat lax; and unlike the weak and
It turns out that there exists a model structure on the category of flows whose weak equivalences are exactly the weak S-homotopy equivalences ([11] and Section 4 of this
ized pullback and finite coproduct preserving functors between categories of permutation representations of finite groups.. Initially surprising to a category theorist, this result
We consider the category ccd(set) whose objects are CCD lattices, and whose arrows are those order functions that have both, a left adjoint and a.. Proposition 5.3 gives us ii)
However, the connection between them and analytic functors is, beyond the category of sets, quite loose: in many-sorted sets Exam- ple 4.4(iii) below demonstrates that a wide
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
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
One can thus replace Open (M ) by a more sophisticated category whose objects are “manifolds with some structure” and whose maps are “structure-preserving embeddings.” (In the
