The act of joining; the thing joined or added.
Used in a Sentence
adjunctions
Definitions, parts of speech, synonyms, and sentence examples for adjunctions.
Editorial note
The Eilenberg-Zilber theorem states, that two functors between chain complexes are adjunctions to each other.
Examples17
Definitions4
Parts of speech1
Quick take
The act of joining; the thing joined or added.
Meaning at a glance
The clearest senses and uses of adjunctions gathered in one view.
(law) The joining of personal property owned by one to that owned by another.
(category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
Definitions
Core meanings and parts of speech for adjunctions.
noun
The act of joining; the thing joined or added.
noun
(law) The joining of personal property owned by one to that owned by another.
noun
(category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent.
noun
(category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.
Example sentences
The Eilenberg-Zilber theorem states, that two functors between chain complexes are adjunctions to each other.
Plotkin and Power did a lot of super technical work on syntax/semantics adjunctions while sorting out the foundations of effect handlers.
In a weaker sense, long emails and single bullet points may have adjunctions between them.
The unison crew is super friendly (Runar once patiently spent 20 minutes trying to explain adjunctions to me, a perfect stranger).
You understand what computational types are and why the adjunctions are ubquitous – and important.
You can generalize relations to profunctors on categories and galois connections to adjunctions.
The real meat behind category theory are things like natural transformations and adjunctions.
And once you learn about adjunctions, monads get even more gorgeous!
How would you prove the tychonoff theorem purely with adjunctions?
In addition, why shouldn't adjunctions be covered at some point?
The first is literally about adjunctions pertaining to combinatorial species whereas the second devotes an entire section to reviewing the theory and stating results that it uses in a way that I don't really understand.
Category theory studies categories and related constructions, such as functors, natural transformations, adjunctions, (co)limits, universal properties, etc.
Quote examples
Most "hard results" in any subfield of math cannot be derived from pure categorical nonsense like adjunctions.
There's also an attempt to use adjunctions to explain "generalization" which might be relevant [1].
Adjunctions can't be studied without category theory (look up "Galois connections" for a history) and they're hard to avoid once we're talking about enough categories of note.
Generally, "adjunctions are everywhere".
Proper noun examples
Adjunctions, for example, are absolutely fundamental to all of maths, but in truth are not really relevant for SWEs.
Frequently asked questions
Short answers drawn from the clearest meanings and examples for this word.
How do you use adjunctions in a sentence?
The Eilenberg-Zilber theorem states, that two functors between chain complexes are adjunctions to each other.
What does adjunctions mean?
The act of joining; the thing joined or added.
What part of speech is adjunctions?
adjunctions is commonly used as noun.