Questions tagged [category-theory]
Category theory is used to formalize mathematics and its concepts as a collection of objects and arrows (also called morphisms). Category theory can be used to formalize concepts of other high-level abstractions such as set theory, ring theory, and group theory. (By Steve Awodey)
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Definition of opposite category
From page 29 of The algebra of programming :
For any category C the opposite category $C^{op}$ is defined to have
the same objects and arrows as C, but the source and target operators
are ...
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Identity in the category of types and functions
In the model of (functional) programming languages as a category where the objects are types and the arrows are functions, I'm trying to really understand what's really the identity arrow.
Barr-Wells ...
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Which fixpoint is Haskell list type?
Let's say that lists are defined as
List a = Nil | Cons a (List a)
Then, in Haskell is List x the greatest or least fixpoint? ...
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Category theory and graphs
Could most categories , or a finite part of them be represented on a subset of a complete graph of N vertices (Kn) which is connected. and partly directed? Could all the axioms of category theory be ...
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About computer science and category theory [duplicate]
I read that Category Theory has alot to do with how programs and information can be organised.Can Category theory simplify various programming strategies? If a specific Category is represented as a ...
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What is a polyad? [closed]
I've read the wikipedia article, but I don't speak category theory (and I'm not sure how to start so I'm just picking something that sounds interesting). So, can someone give me a simple, possibly ...
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What do functions look like, if I stated out with the categoical model of my type theory?
I see how objects in a category stand for types, but where do I find the terms and more specifically the rules which tell me which of them are allowed? When I e.g. consider a Cartesian closed category ...
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How much math background do you need to understand how category theory is applied to Haskell? [duplicate]
Basically, how much math background do you need to understand how category theory is applied to Haskell? If you already have mathematical maturity, can you jump right into it, or should you be ...
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Generalized operators for programming languages
After asking this question on stackoverflow, it has changed slightly. Is there a way to represent a grammar as a basis for a vector space and represent a program as an object that lives in that ...
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What's the correct definition of the $\Upsilon$ category of schedules?
I'm reading this article about game semantics and I'm a bit puzzled with the definition given for $\Upsilon$ in section $3.3$. There are some points that are either unintelligible or that don't make ...
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Category theory (not) for Programming?
After learning Haskell and other not so pure FP languages I decided to read about Category theory. After gaining good understanding of Category theory I started thinking about how the concepts of ...
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The List functor
I have been reading some notes on Category Theory. One question that is posed is to verify the definition of $\operatorname{List}$ is a functor...
$\operatorname{List}(g \circ f) = (\operatorname{...
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Tool/app for learning category theory?
Being a programmer I appreciate the errors given by a compiler for a programming language and come to rely on the compiler's error as a safety net.
In learning category theory I would like to have ...
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Substitution by structural recursion
Following the article's notation, I write $\mathcal{F}$ for the
category of presheaves on a (suitable) category $\mathbb{F}$, $TV$ for the
presheaf of terms, $\delta$ for the context extension, and
$\...
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What is meant by Category theory doesn't yet know how to deal with higher-order functions?
In reading Uday Reddy's answer to What is the relation between functors in SML and Category theory? Uday states
Category theory doesn't yet know how to deal with higher-order
functions. Some day, ...
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What is the relation between functors in SML and Category theory?
Along the same thinking as this statement by Andrej Bauer in this answer
The Haskell community has developed a number of techniques inspired by
category theory, of which monads are best known but ...
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How are programming languages and foundations of mathematics related?
Basically I am aware of three foundations for math
Set theory
Type theory
Category theory
So in what ways are programming languages and foundations of mathematics related?
EDIT
The original ...
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Are monoids useful in optimization?
Many common operations are monoids. Haskell has leveraged this observation to make many higher-order functions more generic (Foldable being one example).
There is ...
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Is Category Theory useful for learning functional programming?
I'm learning Haskell and I'm fascinated by the language. However I have no serious math or CS background. But I am an experienced software programmer.
I want to learn category theory so I can become ...
dan
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Natural occurrences of monads that make use of the category-theoretical framework
Today, a talk by Henning Kerstan ("Trace Semantics for Probabilistic Transition Systems") confronted me with category theory for the first time. He has built a theoretical framework for describing ...
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