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Throughout this thread, let us assume smallness. All functors "are" left adjoints Let $D \xrightarrow{F} C$ be any functor, which induces $$ D \xrightarrow{F} \hat{C}$$ by compositing the ...

Let $T = (t, \mu, \eta)$ be a monad on an object $A$ of a 2-category $\mathcal K$. In The formal theory of monads, Street proves (Theorem 3) that if $l \dashv r$ is the canonical adjunction associated ...

Background I am reviewing some category theory, which I did not learn too well the first time around. One text I am using is Mac Lane's. Near the beginning of the chapter on adjunctions (pg 80), he ...