Tag Archive for Category Theory

Catecon: Identity Is Isomorphism

See diagrams at https://catecon.net/d/hdole/identity and https://catecon.net/d/hdole/isomorphism. Today, let’s define the notions of identity and isomorphism. Then show in Catecon how an identity is an isomorphism. Let’s get morphing! Create a new diagram called identity. CT’s say “The morphism id on an object A in the category D is an identity if for every f with…

Catecon: Internal Definition of Category

See the diagram at https://catecon.net/d/hdole/category The notion of category is fundamental, so how does one describe a category inside another category? Catecon is a categorical console, so we need a good answer. Most gloss over the definition and leave out detailing those ‘evident’ diagrams typically left to the reader or grad student. Who has seen…

Catecon: String Graphs

See the diagram at https://catecon.net/d/hdole/graph In this video we show various string graphs in Catecon. In particular, the origin of the icon for string graphs is given. Let’s get morphing. String graphs, or sometimes referred to as Kelly-Mac Lane graphs, see nLab, are used for coherence in closed categories. In Catecon they visually indicate what…

V Is For Vortex – More Categorical Programming

Vortex, A Categorical Database In the early 90’s I led a product team of three folks to create Vortex, a database for electronic design automation (EDA).  This work at Intergraph Electronics/Dazix/Veribest was based on the categorical programming technique previously developed for the Clipper microprocessor.  As it happens the product was never released.  The one remaining…