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…

# Tag Archive for Category Theory

# 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…

# Catecon YouTube Channel

Created the YouTube channel for Catecon.

# Catecon: Factorial as Morphism

View diagram at https://catecon.net/d/hdole/factorial. In this video the factorial n! is built using only basic morphisms like add and multiply, and categorical operators. The notion of ‘if’ is not builtin, so there’s work to be done! Today we’ll show how to build a factorial morphism using basic functions like add and multiply and categorical operators…

# Catecon: Data Morphisms

Data morphisms in Catecon contain information that can be used in a composite. For example, f(2) = 6. The domain for a data morphism is generally ℕ, but the codomain may have a complex form such as (𝔽×𝔽)×(ℤ×ℤ)×(ℕ×ℕ). The old data morphisms in Catecon were simply a mapping from an index to a value which…

# Catecon Blog October 21, 2018

Factor Morphisms In Catecon a factor morphism is derived from a product domain by listing indices giving factors in the the product hierarchy. This then forms various projections and deltas from the given domain to the codomain. For example, suppose you have a domain of AxBxC, and you want to make two copies of A,…

# Catecon Blog October 15, 2018

Some current details about the development status of Catecon: The Categorical Console. October 15, 2018 New Objects And Named Identities Created a new object panel to replace the old one with all the issues it provided. You could not create a decent named object, like Point say as defined as F*F, and have it act…

# Catecon: Screenshot Of String Shots

A screenshot from Catecon, the Categorical Console, showing basic string shots. Here we start to see the colored chalkings of coherence.

# Catecon: Fibonacci

Let’s try to see the Fibonacci numbers. As you know, the Fibonacci number of n is the Fibonacci number of n-1 plus the Fibonacci number of n-2. Looks like a natural use of recursion so buckle up. Let’s start by having our own Fibonacci diagram. Drag the natural numbers onto the diagram. Control-drag to form…

# Catecon: Factorial

Prior video Catecon: Introduction. My first machine to play on beyond some sticks to rub together (a slide rule) was an Olivetti Programma 101 with magnetic cards. My first program, well, one with loops, was to compute factorials. Let’s do that here, with recursion. Given a natural number n, the factorial of n is n…

# Catecon: Visualizing Coherence In The Categorical Console

Videos for the Categorical Console. Introduction Up to “Hello, world!” “Now, Bob,” I distinctly recall Saunders saying to me. “You have to have good names for your ideas.” I had gone in for our weekly meeting to complain about one of his names, namely that of “central morphisms”. I opined that the “centrality” should extend…

# 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…

# Intro To Categorical Programming

Have You Shorts Or Opens? Categorical programming was applied to the building of the Clipper microprocessor. Read how part of it was done. Beginning work ’84 at Fairchild Semiconductor as a CAD engineer on the Clipper microprocessor, one of the early assignments was to look at a pen plotter. A pen plotter possesses a few…

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