diff --git a/.travis.yml b/.travis.yml
--- a/.travis.yml
+++ b/.travis.yml
@@ -4,9 +4,11 @@
 #
 # For more information, see https://github.com/haskell-CI/haskell-ci
 #
-# version: 0.3.20190425
+# version: 0.9.20191126
 #
+version: ~> 1.0
 language: c
+os: linux
 dist: xenial
 git:
   # whether to recursively clone submodules
@@ -22,6 +24,7 @@
   directories:
     - $HOME/.cabal/packages
     - $HOME/.cabal/store
+    - $HOME/.hlint
 before_cache:
   - rm -fv $CABALHOME/packages/hackage.haskell.org/build-reports.log
   # remove files that are regenerated by 'cabal update'
@@ -31,48 +34,63 @@
   - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.tar
   - rm -fv $CABALHOME/packages/hackage.haskell.org/01-index.tar.idx
   - rm -rfv $CABALHOME/packages/head.hackage
-matrix:
+jobs:
   include:
+    - compiler: ghc-8.10.1
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.10.1","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-8.8.1
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.8.1","cabal-install-3.0"]}}
-      env: GHCHEAD=true
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.8.1","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-8.6.5
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.6.5","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.6.5","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-8.4.4
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.4.4","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.4.4","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-8.2.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.2.2","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.2.2","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-8.0.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-8.0.2","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-8.0.2","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-7.10.3
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.10.3","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.10.3","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-7.8.4
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.8.4","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.8.4","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-7.6.3
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.6.3","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.6.3","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-7.4.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.4.2","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.4.2","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-7.2.2
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.2.2","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.2.2","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-7.0.4
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-7.0.4","cabal-install-2.4"]}}
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-7.0.4","cabal-install-3.0"]}}
+      os: linux
     - compiler: ghc-head
-      addons: {"apt":{"sources":["hvr-ghc"],"packages":["ghc-head","cabal-install-head"]}}
-      env: GHCHEAD=true
+      addons: {"apt":{"sources":[{"sourceline":"deb http://ppa.launchpad.net/hvr/ghc/ubuntu xenial main","key_url":"https://keyserver.ubuntu.com/pks/lookup?op=get&search=0x063dab2bdc0b3f9fcebc378bff3aeacef6f88286"}],"packages":["ghc-head","cabal-install-head"]}}
+      os: linux
   allow_failures:
     - compiler: ghc-head
     - compiler: ghc-7.0.4
     - compiler: ghc-7.2.2
-    - compiler: ghc-8.8.1
+    - compiler: ghc-8.10.1
 before_install:
   - HC=$(echo "/opt/$CC/bin/ghc" | sed 's/-/\//')
+  - WITHCOMPILER="-w $HC"
+  - HADDOCK=$(echo "/opt/$CC/bin/haddock" | sed 's/-/\//')
   - HCPKG="$HC-pkg"
   - unset CC
   - CABAL=/opt/ghc/bin/cabal
   - CABALHOME=$HOME/.cabal
   - export PATH="$CABALHOME/bin:$PATH"
   - TOP=$(pwd)
-  - HCNUMVER=$(( $(${HC} --numeric-version|sed -E 's/([0-9]+)\.([0-9]+)\.([0-9]+).*/\1 * 10000 + \2 * 100 + \3/') ))
+  - "HCNUMVER=$(${HC} --numeric-version|perl -ne '/^(\\d+)\\.(\\d+)\\.(\\d+)(\\.(\\d+))?$/; print(10000 * $1 + 100 * $2 + ($3 == 0 ? $5 != 1 : $3))')"
   - echo $HCNUMVER
   - CABAL="$CABAL -vnormal+nowrap+markoutput"
   - set -o pipefail
@@ -99,35 +117,47 @@
   - echo "$(${HC} --version) [$(${HC} --print-project-git-commit-id 2> /dev/null || echo '?')]"
   - TEST=--enable-tests
   - BENCH=--enable-benchmarks
-  - GHCHEAD=${GHCHEAD-false}
+  - HEADHACKAGE=false
+  - if [ $HCNUMVER -ge 81000 ] ; then HEADHACKAGE=true ; fi
   - rm -f $CABALHOME/config
   - |
-    echo "verbose: normal +nowrap +markoutput"          >> $CABALHOME/config
-    echo "remote-build-reporting: anonymous"            >> $CABALHOME/config
-    echo "remote-repo-cache: $CABALHOME/packages"       >> $CABALHOME/config
-    echo "logs-dir:          $CABALHOME/logs"           >> $CABALHOME/config
-    echo "world-file:        $CABALHOME/world"          >> $CABALHOME/config
-    echo "extra-prog-path:   $CABALHOME/bin"            >> $CABALHOME/config
-    echo "symlink-bindir:    $CABALHOME/bin"            >> $CABALHOME/config
-    echo "installdir:        $CABALHOME/bin"            >> $CABALHOME/config
-    echo "build-summary:     $CABALHOME/logs/build.log" >> $CABALHOME/config
-    echo "store-dir:         $CABALHOME/store"          >> $CABALHOME/config
-    echo "install-dirs user"                            >> $CABALHOME/config
-    echo "  prefix: $CABALHOME"                         >> $CABALHOME/config
-    echo "repository hackage.haskell.org"               >> $CABALHOME/config
-    echo "  url: http://hackage.haskell.org/"           >> $CABALHOME/config
+    echo "verbose: normal +nowrap +markoutput"                                  >> $CABALHOME/config
+    echo "remote-build-reporting: anonymous"                                    >> $CABALHOME/config
+    echo "write-ghc-environment-files: always"                                  >> $CABALHOME/config
+    echo "remote-repo-cache: $CABALHOME/packages"                               >> $CABALHOME/config
+    echo "logs-dir:          $CABALHOME/logs"                                   >> $CABALHOME/config
+    echo "world-file:        $CABALHOME/world"                                  >> $CABALHOME/config
+    echo "extra-prog-path:   $CABALHOME/bin"                                    >> $CABALHOME/config
+    echo "symlink-bindir:    $CABALHOME/bin"                                    >> $CABALHOME/config
+    echo "installdir:        $CABALHOME/bin"                                    >> $CABALHOME/config
+    echo "build-summary:     $CABALHOME/logs/build.log"                         >> $CABALHOME/config
+    echo "store-dir:         $CABALHOME/store"                                  >> $CABALHOME/config
+    echo "install-dirs user"                                                    >> $CABALHOME/config
+    echo "  prefix: $CABALHOME"                                                 >> $CABALHOME/config
+    echo "repository hackage.haskell.org"                                       >> $CABALHOME/config
+    echo "  url: http://hackage.haskell.org/"                                   >> $CABALHOME/config
+    echo "  secure: True"                                                       >> $CABALHOME/config
+    echo "  key-threshold: 3"                                                   >> $CABALHOME/config
+    echo "  root-keys:"                                                         >> $CABALHOME/config
+    echo "    fe331502606802feac15e514d9b9ea83fee8b6ffef71335479a2e68d84adc6b0" >> $CABALHOME/config
+    echo "    1ea9ba32c526d1cc91ab5e5bd364ec5e9e8cb67179a471872f6e26f0ae773d42" >> $CABALHOME/config
+    echo "    2c6c3627bd6c982990239487f1abd02e08a02e6cf16edb105a8012d444d870c3" >> $CABALHOME/config
+    echo "    0a5c7ea47cd1b15f01f5f51a33adda7e655bc0f0b0615baa8e271f4c3351e21d" >> $CABALHOME/config
+    echo "    51f0161b906011b52c6613376b1ae937670da69322113a246a09f807c62f6921" >> $CABALHOME/config
   - |
-    if $GHCHEAD; then
+    if $HEADHACKAGE; then
     echo "allow-newer: $($HCPKG list --simple-output | sed -E 's/([a-zA-Z-]+)-[0-9.]+/*:\1/g')" >> $CABALHOME/config
-    
-    echo "repository head.hackage"                                                        >> $CABALHOME/config
-    echo "   url: http://head.hackage.haskell.org/"                                       >> $CABALHOME/config
+    echo "repository head.hackage.ghc.haskell.org"                                        >> $CABALHOME/config
+    echo "   url: https://ghc.gitlab.haskell.org/head.hackage/"                           >> $CABALHOME/config
     echo "   secure: True"                                                                >> $CABALHOME/config
-    echo "   root-keys: 07c59cb65787dedfaef5bd5f987ceb5f7e5ebf88b904bbd4c5cbdeb2ff71b740" >> $CABALHOME/config
-    echo "              2e8555dde16ebd8df076f1a8ef13b8f14c66bad8eafefd7d9e37d0ed711821fb" >> $CABALHOME/config
-    echo "              8f79fd2389ab2967354407ec852cbe73f2e8635793ac446d09461ffb99527f6e" >> $CABALHOME/config
+    echo "   root-keys: 7541f32a4ccca4f97aea3b22f5e593ba2c0267546016b992dfadcd2fe944e55d" >> $CABALHOME/config
+    echo "              26021a13b401500c8eb2761ca95c61f2d625bfef951b939a8124ed12ecf07329" >> $CABALHOME/config
+    echo "              f76d08be13e9a61a377a85e2fb63f4c5435d40f8feb3e12eb05905edb8cdea89" >> $CABALHOME/config
     echo "   key-threshold: 3"                                                            >> $CABALHOME/config
     fi
+  - |
+    echo "program-default-options"                >> $CABALHOME/config
+    echo "  ghc-options: $GHCJOBS +RTS -M6G -RTS" >> $CABALHOME/config
   - cat $CABALHOME/config
   - rm -fv cabal.project cabal.project.local cabal.project.freeze
   - travis_retry ${CABAL} v2-update -v
@@ -135,17 +165,16 @@
   - rm -rf cabal.project cabal.project.local cabal.project.freeze
   - touch cabal.project
   - |
-    echo 'packages: "."' >> cabal.project
+    echo "packages: ." >> cabal.project
   - |
-    echo "write-ghc-environment-files: always" >> cabal.project
-  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | grep -vE -- '^(bifunctors)$' | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
+  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | (grep -vE -- '^(bifunctors)$' || true) | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
   - cat cabal.project || true
   - cat cabal.project.local || true
   - if [ -f "./configure.ac" ]; then (cd "." && autoreconf -i); fi
-  - ${CABAL} v2-freeze -w ${HC} ${TEST} ${BENCH} | color_cabal_output
+  - ${CABAL} v2-freeze $WITHCOMPILER ${TEST} ${BENCH} | color_cabal_output
   - "cat cabal.project.freeze | sed -E 's/^(constraints: *| *)//' | sed 's/any.//'"
   - rm  cabal.project.freeze
-  - ${CABAL} v2-build -w ${HC} ${TEST} ${BENCH} --dep -j2 all | color_cabal_output
+  - ${CABAL} v2-build $WITHCOMPILER ${TEST} ${BENCH} --dep -j2 all | color_cabal_output
 script:
   - DISTDIR=$(mktemp -d /tmp/dist-test.XXXX)
   # Packaging...
@@ -153,26 +182,27 @@
   # Unpacking...
   - mv dist-newstyle/sdist/*.tar.gz ${DISTDIR}/
   - cd ${DISTDIR} || false
-  - find . -maxdepth 1 -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - find . -maxdepth 1 -type f -name '*.tar.gz' -exec tar -xvf '{}' \;
+  - find . -maxdepth 1 -type f -name '*.tar.gz' -exec rm       '{}' \;
+  - PKGDIR_bifunctors="$(find . -maxdepth 1 -type d -regex '.*/bifunctors-[0-9.]*')"
   # Generate cabal.project
   - rm -rf cabal.project cabal.project.local cabal.project.freeze
   - touch cabal.project
   - |
-    echo 'packages: "bifunctors-*/*.cabal"' >> cabal.project
+    echo "packages: ${PKGDIR_bifunctors}" >> cabal.project
   - |
-    echo "write-ghc-environment-files: always" >> cabal.project
-  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | grep -vE -- '^(bifunctors)$' | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
+  - "for pkg in $($HCPKG list --simple-output); do echo $pkg | sed 's/-[^-]*$//' | (grep -vE -- '^(bifunctors)$' || true) | sed 's/^/constraints: /' | sed 's/$/ installed/' >> cabal.project.local; done"
   - cat cabal.project || true
   - cat cabal.project.local || true
   # Building with tests and benchmarks...
   # build & run tests, build benchmarks
-  - ${CABAL} v2-build -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  - ${CABAL} v2-build $WITHCOMPILER ${TEST} ${BENCH} all | color_cabal_output
   # Testing...
-  - ${CABAL} v2-test -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  - ${CABAL} v2-test $WITHCOMPILER ${TEST} ${BENCH} all | color_cabal_output
   # cabal check...
-  - (cd bifunctors-* && ${CABAL} -vnormal check)
+  - (cd ${PKGDIR_bifunctors} && ${CABAL} -vnormal check)
   # haddock...
-  - ${CABAL} v2-haddock -w ${HC} ${TEST} ${BENCH} all | color_cabal_output
+  - ${CABAL} v2-haddock $WITHCOMPILER --with-haddock $HADDOCK ${TEST} ${BENCH} all | color_cabal_output
 
-# REGENDATA ["--output=.travis.yml","--config=cabal.haskell-ci","cabal.project"]
+# REGENDATA ("0.9.20191126",["--output=.travis.yml","--config=cabal.haskell-ci","cabal.project"])
 # EOF
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,8 @@
+5.5.6 [2019.11.26]
+------------------
+* Add `Category`, `Arrow`, `ArrowChoice`, `ArrowLoop`, `ArrowZero`, and
+  `ArrowPlus` instances for `Data.Bifunctor.Product`.
+
 5.5.5 [2019.08.27]
 ------------------
 * Add `Eq{1,2}`, `Ord{1,2}`, `Read{1,2}`, and `Show{1,2}` instances for data
diff --git a/bifunctors.cabal b/bifunctors.cabal
--- a/bifunctors.cabal
+++ b/bifunctors.cabal
@@ -1,6 +1,6 @@
 name:          bifunctors
 category:      Data, Functors
-version:       5.5.5
+version:       5.5.6
 license:       BSD3
 cabal-version: >= 1.8
 license-file:  LICENSE
@@ -24,6 +24,7 @@
              , GHC == 8.4.4
              , GHC == 8.6.5
              , GHC == 8.8.1
+             , GHC == 8.10.1
 extra-source-files:
   .travis.yml
   CHANGELOG.markdown
@@ -59,7 +60,7 @@
     base-orphans        >= 0.5.2 && < 1,
     comonad             >= 4     && < 6,
     containers          >= 0.1   && < 0.7,
-    template-haskell    >= 2.4   && < 2.16,
+    template-haskell    >= 2.4   && < 2.17,
     th-abstraction      >= 0.3   && < 0.4,
     transformers        >= 0.2   && < 0.6
 
diff --git a/src/Data/Bifunctor/Product.hs b/src/Data/Bifunctor/Product.hs
--- a/src/Data/Bifunctor/Product.hs
+++ b/src/Data/Bifunctor/Product.hs
@@ -37,6 +37,8 @@
 import Control.Applicative
 #endif
 
+import qualified Control.Arrow as A
+import Control.Category
 import Data.Biapplicative
 import Data.Bifoldable
 import Data.Bifunctor.Functor
@@ -58,6 +60,8 @@
 import Data.Functor.Classes
 #endif
 
+import Prelude hiding ((.),id)
+
 -- | Form the product of two bifunctors
 data Product f g a b = Pair (f a b) (g a b)
   deriving ( Eq, Ord, Show, Read
@@ -148,3 +152,29 @@
   biextract (Pair _ q) = q
   biduplicate pq@(Pair p _) = Pair p pq
   biextend f pq@(Pair p _) = Pair p (f pq)
+
+instance (Category p, Category q) => Category (Product p q) where
+  id = Pair id id
+  Pair x y . Pair x' y' = Pair (x . x') (y . y') 
+
+instance (A.Arrow p, A.Arrow q) => A.Arrow (Product p q) where
+  arr f = Pair (A.arr f) (A.arr f)
+  first (Pair x y) = Pair (A.first x) (A.first y)
+  second (Pair x y) = Pair (A.second x) (A.second y)
+  Pair x y *** Pair x' y' = Pair (x A.*** x') (y A.*** y')
+  Pair x y &&& Pair x' y' = Pair (x A.&&& x') (y A.&&& y')
+
+instance (A.ArrowChoice p, A.ArrowChoice q) => A.ArrowChoice (Product p q) where
+  left (Pair x y) = Pair (A.left x) (A.left y)
+  right (Pair x y) = Pair (A.right x) (A.right y)
+  Pair x y +++ Pair x' y' = Pair (x A.+++ x') (y A.+++ y')
+  Pair x y ||| Pair x' y' = Pair (x A.||| x') (y A.||| y')  
+
+instance (A.ArrowLoop p, A.ArrowLoop q) => A.ArrowLoop (Product p q) where
+  loop (Pair x y) = Pair (A.loop x) (A.loop y)
+
+instance (A.ArrowZero p, A.ArrowZero q) => A.ArrowZero (Product p q) where
+  zeroArrow = Pair A.zeroArrow A.zeroArrow
+
+instance (A.ArrowPlus p, A.ArrowPlus q) => A.ArrowPlus (Product p q) where
+  Pair x y <+> Pair x' y' = Pair (x A.<+> x') (y A.<+> y')