Live briefing
Everything about Coproduct
Category-theoretic construction
In category theory, the coproduct, or categorical sum, is a construction which includes as examples the disjoint union of sets and of topological spaces, the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific" object to which each object in the family admits a morphism. It is the category-theoretic dual notion to the categorical product, which means the definition is the same as the product but with all arrows reversed. Despite this seemingly innocuous change in the name and notation, coproducts can be and typically are dramatically different from products within a given category. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: CoproductA 5-minute orientation
- Skim a recent paper: Microencapsulation by Spray Drying and Antioxidant Activity of Phenolic Compounds from Tucuma Coproduct (Astrocaryum vulgare Mart.) AlmondsInfluential work since 2022
- Pick up a classic book: Asia-Pacific Film Co-productionsThe most-reprinted book on the subject
- Read the landmark paper: The Techno-Economic Basis for Coproduct Manufacturing To Enable Hydrocarbon Fuel Production from Lignocellulosic BiomassCited 146 times
- Go sideways: Product (category theory)A closely related topic
- Go sideways: Limit (category theory)A closely related topic
📖 Definitions
Noun Any of multiple products that are produced at the same time, or by the same process.
Noun The colimit of two (or more) objects, without regard to any morphisms between them.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Techno-Economic Basis for Coproduct Manufacturing To Enable Hydrocarbon Fuel Production from Lignocellulosic Biomass
Detection of Formate, Rather than Carbon Monoxide, As the Stoichiometric Coproduct in Conversion of Fatty Aldehydes to Alkanes by a Cyanobacterial Aldehyde Decarbonylase
Coproduct and star product in field theories on Lie-algebra noncommutative space-times
PHA bioplastic: A value‐added coproduct for biomass biorefineries
Coproduct market analysis and water footprint of simulated commercial algal biorefineries
Short communication: Composition of coproduct streams from dairy processing: Acid whey and milk permeate
Quercetin and Isorhamnetin Glycosides in Onion (Allium cepa L.): Varietal Comparison, Physical Distribution, Coproduct Evaluation, and Long-Term Storage Stability
Coproduct Technologies: Product Line Design and Process Innovation
🆕 Influential since 2022
Microencapsulation by Spray Drying and Antioxidant Activity of Phenolic Compounds from Tucuma Coproduct (Astrocaryum vulgare Mart.) Almonds
THE IMPORTANCE OF GEOLOGY IN ASSESSING BY- AND COPRODUCT METAL SUPPLY POTENTIAL; A CASE STUDY OF ANTIMONY, BISMUTH, SELENIUM, AND TELLURIUM WITHIN THE COPPER PRODUCTION STREAM
Implications of coproduction technology on waste management: Who can benefit from the coproduct made of leftover materials?
Effect of Temperature and pH on Microbial Communities Fermenting a Dairy Coproduct Mixture
Life Cycle Analysis and Operating Cost Assessment of a Carbon Negative Catalytic Pyrolysis Technique Using a Spent Aluminum Hydroxide Nanoparticle Adsorbent-Derived Catalyst: Insights into Coproduct Utilization and Sustainability
📚 Books worth reading
Asia-Pacific Film Co-productionsDal Yong Jin, Wendy Su · 2019
Contemporary Sino-French CinemasMichelle E. Bloom, Sheldon H. Lu · 2016
INTERNATIONAL ADVENTURESTim Bergfelder · 2004
German Film after GermanyRandall Halle · 2008- 📕Cinema of CollaborationMariana Ivanova · 2019
The Euro-American cinemaPeter Lev · 1993- 📕The fine art of co-producingPer Neumann · 2002
- 📕Zi ben, wen huawen hua : Zhongguo dian ying de"po" yu "li" : xin shi ji zhong wai "he pai pian" xue shu yan tao hui (2014 Shanghai xi ju xue yuan) Zi ben · 2015
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Product (category theory) In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas…
- Limit (category theory) In category theory, a branch of mathematics, the abstract notion of a limit captures the essential properties of universal constructions such as products…
- Cartesian monoidal category In mathematics, specifically in the field known as category theory, a monoidal category where the monoidal ("tensor") product is the categorical product…
- Cartesian closed category In category theory, a category is Cartesian closed if, roughly speaking, any morphism defined on a product of two objects can be naturally identified with…
- Direct limit In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific…
- Adjoint functors In mathematics, specifically category theory, adjunction is a relationship that two functors may exhibit, intuitively corresponding to a weak form of equivalenc…
- Presheaf with transfers In algebraic geometry, a presheaf with transfers is, roughly, a presheaf that, like cohomology theory, comes with pushforwards, “transfer” maps. Precisely…
- Quotient category In mathematics, a quotient category is a category obtained from another category by identifying sets of morphisms. Formally, it is a quotient object in…