# morphisms Published articles for morphisms. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## Category theory DevFeed: [Category theory]() Original publisher: [Read original article]() Published: 2020-04-26T00:00:00Z Content type: tutorial Language: en Sources: [Vasya Drobushkov]() Topics: [Category Theory](), [Programming]() Tags: [category-theory](), [morphisms](), [object](), [programming](), [theory]() ### AI overview A personal synopsis of category theory covering categories, objects, morphisms, composition, universal constructions, order relations, monoids, terminal and initial objects, products, sums, and semirings. It also connects products and sums to programming concepts such as pairs, Either, and algebraic data types. ### Source excerpt Source Disclaimer This is short synopsis of great set of lectures. What is written here is by no means true, one should refer to original lectures or some books etc. This is written mostly for myself in case I wanted to revisit the topic in the future. Everything below is not "what it is" but mostly "how I understood that". So, there might be mistakes and so on. Category Category consists of: ## Functoriality in Category Theory: Mappings That Preserve Morphisms DevFeed: [Functoriality in Category Theory: Mappings That Preserve Morphisms]() Original publisher: [Read original article]() Published: 2013-07-14T10:03:29Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Category Theory](), [Mathematics](), [Math and Logic]() Tags: [categories](), [category-theory](), [coproducts](), [functor](), [homology](), [ml](), [morphisms](), [universal-properties]() ### AI overview This tutorial introduces functoriality in category theory. It explains functors as mappings between categories that assign objects and morphisms while preserving identity morphisms and composition, with homology as an example of a functorial construction. ### Source excerpt Last time we worked through some basic examples of universal properties, specifically singling out quotients, products, and coproducts. There are many many more universal properties that we will mention as we encounter them, but there is one crucial topic in category theory that we have only hinted at: functoriality. As we've repeatedly stressed, the meat of category theory is in the morphisms. One natural question one might ask is, what notion of morphism is there between categories themselves? ## Universal Properties DevFeed: [Universal Properties]() Original publisher: [Read original article]() Published: 2013-05-24T14:53:25Z Content type: tutorial Language: en Sources: [Jeremy Kun]() Topics: [Category Theory](), [Mathematics](), [function](), [object]() Tags: [categories](), [category-theory](), [coproducts](), [examples](), [function](), [mathematics](), [ml](), [morphisms](), [object](), [product](), [programming](), [quotients](), [types](), [universal-properties]() ### AI overview This tutorial introduces universal properties in category theory, defining initial, final, and zero objects through unique morphisms. It illustrates the concepts with examples from mathematics and Set, and discusses constructing programs related to these properties. ### Source excerpt Previously in this series we've seen the definition of a category and a bunch of examples, basic properties of morphisms, and a first look at how to represent categories as types in ML. In this post we'll expand these ideas and introduce the notion of a universal property. We'll see examples from mathematics and write some programs which simultaneously prove certain objects have universal properties and construct the morphisms involved. ## Properties of Morphisms DevFeed: [Properties of Morphisms]() Original publisher: [Read original article]() Published: 2013-05-15T12:43:42Z Content type: article Language: en Sources: [Jeremy Kun]() Topics: [Category Theory](), [Mathematics]() Tags: [categories](), [epimorphism](), [examples](), [introduction](), [mathematics](), [monomorphism](), [morphisms](), [universal-properties]() ### AI overview A mathematical introduction to morphisms in category theory, focusing on isomorphisms and their role in describing when objects are considered the same. It defines isomorphisms and begins examining them in Set. ### Source excerpt This post is mainly mathematical. We left it out of our introduction to categories for brevity, but we should lay these definitions down and some examples before continuing on to universal properties and doing more computation. The reader should feel free to skip this post and return to it later when the words "isomorphism," "monomorphism," and "epimorphism" come up again. Perhaps the most important part of this post is the description of an isomorphism.