In algebra, given a 2-
monad
Monad may refer to:
Philosophy
* Monad (philosophy), a term meaning "unit"
**Monism, the concept of "one essence" in the metaphysical and theological theory
** Monad (Gnosticism), the most primal aspect of God in Gnosticism
* ''Great Monad'', an ...
''T'' in a
2-category
In category theory in mathematics, a 2-category is a category with "morphisms between morphisms", called 2-morphisms. A basic example is the category Cat of all (small) categories, where a 2-morphism is a natural transformation between functors.
...
, a pseudoalgebra for ''T'' is a 2-category-version of
algebra for ''T'', that satisfies the laws up to
coherent isomorphism
In mathematics, specifically in homotopy theory and (higher) category theory, coherency is the standard that equalities or diagrams must satisfy when they hold "up to homotopy" or "up to isomorphism".
The adjectives such as "pseudo-" and "lax-" ...
s.
See also
*
Operad
In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad O, one define ...
Notes
References
*
Further reading
*
External links
*https://ncatlab.org/nlab/show/pseudoalgebra+for+a+2-monad
*https://golem.ph.utexas.edu/category/2014/06/codescent_objects_and_coherenc.html
Adjoint functors
Abstract algebra
Category theory
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