Categories of matrices #178
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Affects the theories of SMCs in additive notation.
Refactor theory of linear functions (functional fragment of GLA) to inherit from this theory.
To avoid confusion once we have theories of additive and semiadditive categories.
The latter was changed to use additive notation. The theory of GLA now inherits the theory of abelian bicategories of relations.
Leads to ambiguity when multiple monoidal products are available. Instead, use `swap` in the additive case.
Also fix missing imports in wiring diagrams module.
jpfairbanks
reviewed
Jun 26, 2020
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Adds support for categories of matrices, both dense and sparse, over a commutative rig. This includes the rig of booleans, paving the way for support for
FinRel.The opportunity is also taken to clean up the hierarchy of theories for relational structures, so as to eventually have a consistent interface for finite relations and linear relations. In particular, the theory for GLA now inherits that of abelian bicategories of relations (relevant to @jpfairbanks, @bosonbaas). Finally, a number of theories related to distributive monoidal structures are added. In a subsequent PR, this will be used to define the theory of distributive bicategories of relations.