Everything about Comma category
Mathematics construct
In mathematics, a comma category is a construction in category theory. It provides another way of looking at morphisms: instead of simply relating objects of a category to one another, morphisms become objects in their own right. This notion was introduced in 1963 by F. W. Lawvere, although the technique did not become generally known until many years later. Several mathematical concepts can be treated as comma categories, such as the special case of a slice category. Comma categories also guarantee the existence of some limits and colimits. The name comes from the notation originally used by Lawvere, which involved the comma punctuation mark. The name persists even though standard notation has changed, since the use of a comma as an operator is potentially confusing, and even Lawvere disliked the uninformative term "comma category". Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Comma categoryA 5-minute orientation
- Skim a recent paper: Lax comma categories of ordered setsInfluential work since 2022
- Pick up a classic book: An Alpine expedition through algebraic topologyThe most-reprinted book on the subject
- Read the landmark paper: Comma categories in representation theoryCited 9 times
- Go sideways: Topological functorA closely related topic
- Go sideways: Lawvere's fixed-point theoremA closely related topic
📖 Definitions
Noun A category built out of a pair of functors that have the same codomain.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Comma categories in representation theory
Fraïssé Limits in Comma Categories
Cotorsion pairs in comma categories
Functors induced by comma categories
On Adjointness of Comma Categories
Topological Lax Comma Categories
🆕 Influential since 2022
📚 Books worth reading
- 📕An Alpine expedition through algebraic topologySwitzerland) Arolla Conference on Algebraic Topology (4th 2012 Arolla · 2014
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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