scholarly journals Wiring diagrams as normal forms for computing in symmetric monoidal categories

2021 ◽  
Vol 333 ◽  
pp. 49-64
Author(s):  
Evan Patterson ◽  
David I. Spivak ◽  
Dmitry Vagner
Keyword(s):  
Normal Forms ◽  
Monoidal Categories ◽  
Symmetric Monoidal Categories

Trace and Duality in Symmetric Monoidal Categories

K-Theory ◽  
2005 ◽  
Vol 35 (3-4) ◽  
pp. 273-339 ◽  
Author(s):  
Andrew Nicas
Keyword(s):  
Monoidal Categories ◽  
Symmetric Monoidal Categories

scholarly journals Galois Theory in Symmetric Monoidal Categories

1999 ◽  
Vol 220 (1) ◽  
pp. 174-187 ◽  
Author(s):  
George Janelidze ◽  
Ross Street
Keyword(s):  
Galois Theory ◽  
Monoidal Categories ◽  
Symmetric Monoidal Categories

scholarly journals Strong Concatenable Processes: An Approach to the Category of Petri Net Computations

1994 ◽  
Vol 1 (33) ◽  
Author(s):  
Vladimiro Sassone
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Monoidal Categories ◽  
Commutative Monoids ◽  
Precise Sense ◽  
Abstract Description ◽  
Symmetric Monoidal Categories

We introduce the notion of <em>strong concatenable process</em> for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a <em> functor</em> Q[_] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories with free non-commutative monoids of objects, in the precise sense that, for each net N, the strong concatenable processes of N are isomorphic to the arrows of Q[N]. This yields an axiomatization of the causal behaviour of Petri nets in terms of symmetric strict monoidal categories.<br /> <br />In addition, we identify a <em>coreflection</em> right adjoint to Q[_] and we characterize its replete image in the category of symmetric monoidal categories, thus yielding an abstract description of the category of net computations.

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