منابع مشابه
Medial commutativity
It is shown that all the assumptions for symmetric monoidal categories flow out of a unifying principle involving natural isomorphisms of the type (A ∧B) ∧ (C ∧D) → (A ∧ C) ∧ (B ∧D), called medial commutativity. Medial commutativity in the presence of the unit object enables us to define associativity and commutativity natural isomorphisms. In particular, Mac Lane’s pentagonal and hexagonal coh...
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In the Map-Reduce programming model for data parallel computation in a cloud environment, the reducer phase is responsible for computing an output key-value pair, given a sequence of input values associated with a particular key. Because of non-determinism in transmitting key-value pairs over the network, the inputs may not arrive at a reducer in a fixed order. This gives rise to the reducer co...
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In this work we present a new sampling-based “black box” inference approach for learning the behaviors of a library component. As an application, we focus on the problem of automatically learning commutativity specifications of data structures. This is a very challenging problem, yet important, as commutativity specifications are fundamental to program analysis, concurrency control and even low...
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We show, using the no–disentanglement theorem, that to teleport (exactly) any set of non–commuting states (i.e., a set containing at least two non–commuting states), it is necessary to have an entangled channel. We further show that to teleport any set of commuting states it is sufficient to have a classically correlated channel. Using this result we provide a simple proof of the fact that any ...
متن کاملAssociativity as commutativity
It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric or braided strictly monoidal categories, where associativity arrows are identities. Mac Lane’s pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality an...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2016
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2015.09.003