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(Our previous work has only dealt with the theory of opetopes.) We then use results of [12] to prove that the category of opetopic sets is indeed equivalent to the category
We saw in the prologue that the comonad Path on Cat has as its coalgebras free categories on graphs (the category of coalgebras is equivalent to the category of graphs), and that
If p ≥ 3, it follows from Theorem 9 that the category of finite flat group schemes over Spec R is equivalent to the category of Breuil modules (the argument for this is the same as
In the cases of Example 2.6, the given regular epimorphisms are not effective descent morphisms but also do not satisfy projectivity. In fact, in both cases, being an effective
We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre-Hilbert spaces
Every atomic Dedekind category R with relational sums and subobjects is equivalent to a category of matrices over a suitable basis.. This basis is the full proper subcategory induced
A complete and cocomplete category B is equivalent to an essential localization of a presheaf category if and only if it is infinitary extensive and satisfies conditions (LM),
Existing support tools are usually oriented on: supporting the installation of IT systems, order-oriented modeling of production systems, material # ow analysis, simulation, or
