This is a catalogue of the major functions, type classes, and data types in Cats. It serves as a bird's-eye view of each class capabilities. It is also intended as a go-to reference for Cats users, who may not recall the answer to questions like these:

The signatures and type-classes have been simplified, are described below. If you want a printable version, you can also check out this cats-cheatsheet.

WARNING: this page is written manually, and not automatically generated, so many things may be missing. If you find a mistake, or addition, please submit a PR following the guidelines below.

Type-Classes over an F[_]


Type Method Name
F[A] => F[Unit] void
F[A] => B => F[B] as
F[A] => (A => B) => F[B] map
F[A] => (A => B) => F[(A,B)] fproduct
F[A] => (A => B) => F[(B,A)] fproductLeft
F[A] => B => F[(B, A)] tupleLeft
F[A] => B => F[(A, B)] tupleRight
(A => B) => (F[A] => F[B]) lift


Type Method Name Symbol
F[A] => F[B] => F[A] productL <*
F[A] => F[B] => F[B] productR *>
F[A] => F[B] => F[(A,B)] product
F[A => B] => F[A] => F[B] ap <*>
F[A => B => C] => F[A] => F[B] => F[C] ap2
F[A] => F[B] => (A => B => C) => F[C] map2


Type Method Name Notes
A => F[A] pure
=> F[Unit] unit
Boolean => F[Unit] => F[Unit] whenA Performs effect iff condition is true
unlessA Adds effect iff condition is false


Type Method Name
F[F[A]] => F[A] flatten
F[A] => (A => F[B]) => F[B] flatMap
F[A] => (A => F[B]) => F[(A,B)] mproduct
F[Boolean] => F[A] => F[A] => F[A] ifM
F[A] => (A => F[B]) => F[A] flatTap


Type Method Name Notes
F[A] => (A => Boolean) => F[A] filter
F[A] => (A => Option[B]) => F[B] mapFilter
F[A] => (A => B) => F[B] collect The A => B is a PartialFunction
F[Option[A]] => F[A] flattenOption


The source code of Cats uses the E type variable for the error type.

Type Method Name Notes
E => F[A] raiseError
F[A] => F[Either[E,A]] attempt
F[A] => (E => A) => F[A] handleError
F[A] => (E => F[A]) => F[A] handleErrorWith
F[A] => (E => A) => F[A] recover The E => A is a PartialFunction.
F[A] => (E => F[A]) => F[A] recoverWith The E => F[A] is a PartialFunction.
F[A] => (E => F[Unit]) => F[A] onError The E => F[Unit] is a PartialFunction.
Either[E,A] => F[A] fromEither
Option[A] => E => F[A] liftFromOption


Like the previous section, we use the E for the error parameter type.

Type Method Name Notes
F[A] => E => (A => Boolean) => F[A] ensure
F[A] => (A => E) => (A => Boolean) => F[A] ensureOr
F[A] => (E => E) => F[A] adaptError The E => E is a PartialFunction.
F[Either[E,A]] => F[A] rethrow


Type Method Name Constraints
F[A] => Boolean isEmpty
F[A] => Boolean nonEmpty
F[A] => Long size
F[A] => (A => Boolean) => Boolean forall
F[A] => (A => Boolean) => Boolean exists
F[A] => A unorderedFold A: CommutativeMonoid
F[A] => (A => B) => B unorderedFoldMap B: CommutativeMonoid


Type Method Name Constraints
F[A] => A fold A: Monoid
F[A] => B => ((B,A) => B) => F[B] foldLeft
F[A] => (A => B) => B foldMap B: Monoid
F[A] => (A => G[B]) => G[B] foldMapM G: Monad and B: Monoid
F[A] => (A => B) => Option[B] collectFirst The A => B is a PartialFunction
F[A] => (A => Option[B]) => Option[B] collectFirstSome
F[A] => (A => G[B]) => G[Unit] traverse_ G: Applicative
F[G[A]] => G[Unit] sequence_ G: Applicative
F[A] => (A => Either[B, C] => (F[B], F[C]) partitionEither G: Applicative


Type Method Name Constraints
F[A] => ((A,A) => A) => A reduceLeft
F[A] => A reduce A: Semigroup


Type Method Name Constraints
F[G[A]] => G[F[A]] sequence G: Applicative
F[A] => (A => G[B]) => G[F[B]] traverse G: Applicative
F[A] => (A => G[F[B]]) => G[F[B]] flatTraverse F: FlatMap and G: Applicative
F[G[F[A]]] => G[F[A]] flatSequence G: Applicative and F: FlatMap
F[A] => F[(A,Int)] zipWithIndex
F[A] => ((A,Int) => B) => F[B] mapWithIndex
F[A] => ((A,Int) => G[B]) => G[F[B]] traverseWithIndex F: Monad


Constructors and wrappers

Data Type is an alias or wrapper of
OptionT[F[_], A] F[Option[A]]
EitherT[F[_], A, B] F[Either[A,B]
Kleisli[F[_], A, B] A => F[B]
Reader[A, B] A => B
ReaderT[F[_], A, B] Kleisli[F, A, B]
Writer[A, B] (A,B)
WriterT[F[_], A, B] F[(A,B)]
Tuple2K[F[_], G[_], A] (F[A], G[A])
EitherK[F[_], G[_], A] Either[F[A], G[A]]
FunctionK[F[_], G[_]] F[X] => G[X] for every X
F ~> G Alias of FunctionK[F, G]


For convenience, in these types we use the symbol OT to abbreviate OptionT.

Type Method Name Constraints
=> OT[F, A] none F: Applicative
A => OT[F, A] some or pure F: Applicative
F[A] => OT[F, A] liftF F: Functor
OT[F, A] => F[Option[A]] value
OT[F, A] => (A => B) => OT[F, B] map F: Functor
OT[F, A] => (F ~> G) => OT[G, B] mapK
OT[F, A] => (A => Option[B]) => OT[F, B] mapFilter F: Functor
OT[F, A] => B => (A => B) => F[B] fold or cata
OT[F, A] => (A => OT[F, B]) => OT[F,B] flatMap
OT[F, A] => (A => F[Option[B]]) => F[B] flatMapF F: Monad
OT[F, A] => A => F[A] getOrElse F: Functor
OT[F, A] => F[A] => F[A] getOrElseF F: Monad
OT[F, A] => OT[F, A] => OT[F, A]


Here, we use ET to abbreviate EitherT; and we use A and B as type variables for the left and right sides of the Either.

Type Method Name Constraints
A => ET[F, A, B] leftT F: Applicative
B => ET[F, A, B] rightT F: Applicative
pure F: Applicative
F[A] => ET[F, A, B] left F: Applicative
F[B] => ET[F, A, B] right F: Applicative
liftF F: Applicative
Either[A, B] => ET[F, A, B] fromEither F: Applicative
Option[B] => A => ET[F, A, B] fromOption F: Applicative
F[Option[B]] => A => ET[F, A, B] fromOptionF F: Functor
F[Option[B]] => F[A] => ET[F, A, B] fromOptionM F: Monad
Boolean => B => A => ET[F, A, B] cond F: Applicative
ET[F, A, B] => (A => C) => (B => C) => F[C] fold F: Functor
ET[F, A, B] => ET[F, B, A] swap F: Functor
ET[F, A, A] => F[A] merge

Kleisli (or ReaderT)

Here, we use Ki as a short-hand for Kleisli.

Type Method Name Constraints
Ki[F, A, B] => (A => F[B]) run
Ki[F, A, B] => A => F[B] apply
A => Ki[F, A, A] ask F: Applicative
B => Ki[F, A, B] pure F: Applicative
F[B] => Ki[F, A, B] liftF
Ki[F, A, B] => (C => A) => Ki[F, C, B] local
Ki[F, A, B] => Ki[F, A, A] tap
Ki[F, A, B] => (B => C) => Ki[F, A, C] map
Ki[F, A, B] => (F ~> G) => Ki[G, A, B] mapK
Ki[F, A, B] => (F[B] => G[C]) => Ki[F, A, C] mapF
Ki[F, A, B] => Ki[F, A, F[B]] lower

Type Classes for types F[_, _]


Type Method Name
F[A,B] => (A => C) => F[C,B] leftMap
F[A,B] => (B => D) => F[A,D] .rightFunctor and .map
F[A,B] => (A => C) => (B => D) => F[C,D] bimap


Type Method Name
F[A, B] => (B => C) => F[A, C] rmap
F[A, B] => (C => A) => F[C, B] lmap
F[A, B] => (C => A) => (B => D) => F[C,D] dimap

Strong Profunctor

Type Method Name
F[A, B] => F[(A,C), (B,C)] first
F[A, B] => F[(C,A), (C,B)] second

Compose, Category, Choice

Type Method Name Symbol
F[A, B] => F[C, A] => F[C, B] compose <<<
F[A, B] => F[B, C] => F[A, C] andThen >>>
=> F[A,A] id
F[A, B] => F[C, B] => F[Either[A, C], B] choice `
=> F[ Either[A, A], A] codiagonal


Type Method Name Symbol
(A => B) => F[A, B] lift
F[A,B] => F[C,D] => F[(A,C), (B,D)] split ***
F[A,B] => F[A,C] => F[A, (B,C)] merge &&&


Type Method Name Symbol
F[A,B] => F[C,D] => F[Either[A, C], Either[B, D]] choose +++
F[A,B] => F[Either[A, C], Either[B, C]] left
F[A,B] => F[Either[C, A], Either[C, B]] right


Because Сats is a Scala library and Scala has many knobs and switches, the actual definitions and the implementations of the functions and type-classes in Сats can be a bit obfuscated at first. To alleviate this, in this glossary we focus on the plain type signatures of the method, and ignore many of the details from Scala. In particular, in our type signatures: