pseudomonad

== English == === Etymology 1 === From pseudo- +‎ monad; a trivialized form of the scientific name Pseudomonas. ==== Noun ==== pseudomonad (plural pseudomonads) Any of many bacteria of the family Pseudomonadaceae, some of which are pathogenic ===== Derived terms ===== ===== Related terms ===== pseud ===== Translations ===== ==== References ==== pseudomonad on Wikipedia.Wikipedia Pseudomonadaceae on Wikispecies.Wikispecies Category:Pseudomonadaceae on Wikimedia Commons.Wikimedia Commons === Etymology 2 === From pseudo- +‎ monad. ==== Noun ==== pseudomonad (plural pseudomonads) (category theory) A weak generalization of a monad on a Gray-category or 2-category (or more generally a weak 2-category) C {\displaystyle {\mathcal {C}}} consists of a 2-functor (in particular, if it is a functor on a weak 2-category, it is a pseudo-functor) T : C → C {\displaystyle T:{\mathcal {C}}\rightarrow {\mathcal {C}}} equipped with pseudonatural transformations μ : T 2 → T {\displaystyle \mu :T^{2}\rightarrow T} and η : I d → T {\displaystyle \eta :\mathrm {Id} \rightarrow T} which satisfy the monad laws up to coherent invertible modifications.