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Cat Blog
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Jade Master's Blog About Categories
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Cat Blog – Jade Master's Blog About Categories Skip to content Cat Blog Jade Master's Blog About Categories Menu Home Contact Can enriched category theory compute? An experiment in Idris2 This post will be an implementation of some ideas from V-enriched category theory when V is a semiring. Usually enrichment is taken in a symmetric monoidal closed category . Semiring-enrichment is a a special case where the and form a strict semiring and V happens to be a poset. In this special case, enriched category theory can be phrased in terms of linear algebra. If you want a very abstract reason for this, it’s because a V-enriched category is a monad in the bicategory Mat(V) of V-valued matrices. When V is just a semiring, then the composition and coproduct in Mat(V) are the standard matrix multiplication and sum. First we’ll need to implement some basic linear algebra over a semiring. Let’s define a semiring as an algebra for a certain polynomial functor data...
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