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V-localizations and V-triples
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madnight committed Feb 24, 2024
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Expand Up @@ -36,6 +36,9 @@ A curated list of awesome Category Theory resources.
* [Limit Monads in Categories](https://github.com/CategoryTheoryArchive/archive/blob/main/resources/1967_kock_limit-monads.pdf) - The work introduces the notion that the category of complete categories is monadic over the category of all categories, utilizing a family of monads associated with various index categories to define "completeness." A significant portion of the thesis is dedicated to defining associative and regular associative colimits, arguing for their naturalness and importance in category theory. Dissertation by Anders Jungersen Kock (1967)

* [On the concreteness of certain categories](https://github.com/CategoryTheoryArchive/archive/blob/main/resources/1969_freyd_concreteness-certain.pdf) - This work discusses the concept of concreteness in categories, stating that a concrete category is one with a faithful functor to the category of sets, and must be locally-small. He highlights the homotopy category of spaces as a prime example of a non-concrete category, emphasizing its abstract nature due to the irrelevance of individual points within spaces and the inability to distinguish non-homotopic maps through any functor into concrete categories. Peter Freyd (1969)

* [V-localizations and V-triples](https://github.com/CategoryTheoryArchive/archive/blob/main/resources/1970_wolff_v-localizations-v-triples.pdf) This work focuses on two primary objectives within category theory. The first goal is to define and study Y-localizations of Y-categories, using a model akin to localizations in ordinary categories, involving certain conditions related to isomorphisms and the existence of unique Y-functors. The second aim is to explore the relationship between Y-localizations and V-triples, presenting foundational theories and examples to elucidate these concepts. Harvey Eli Wolff's dissertation (1970)

## Articles

#### Bayesian/Causal inference
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