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We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...
We outline our recent results on bicovariant differential calculi on co-quasitriangular Hopf algebras, in particular that if is a quantum tangent space (quantum Lie algebra) for a CQT Hopf algebra A, then the space is a braided Lie algebra in the category of A-comodules. An important consequence of this is that the universal enveloping algebra is a bialgebra in the category of A-comodules.
We present a categorical formulation
of the rewriting of possibly cyclic term graphs, based on a
variation of algebraic 2-theories. We show that
this presentation is equivalent to the well-accepted
operational definition proposed by Barendregt et al. – but
for the
case of circular redexes , for which we propose (and
justify formally) a different treatment.
The categorical framework allows us to model in a concise way
also automatic garbage collection
and rules
for sharing/unsharing and...
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