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Kleisli category
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<p>In <a href="/facts/Category_theory/6zS3DXPa">category theory</a>, a Kleisli category is a <a href="/facts/Category_(mathematics)/7WzxUThf">category</a> naturally associated to any <a href="/facts/Monad_(category_theory)/6fX10Qrx">monad</a> <i>T</i>. It is equivalent to the category of <a href="/facts/Free_object/VxL28y8B">free</a> <a href="/facts/Monad_(category_theory)/6fX10Qrx"><i>T</i>-algebras</a>. The Kleisli category is one of two extremal solutions to the question: "<i>Does every monad arise from an <a href="/facts/Adjunction_(category_theory)/bJ1P7AN2">adjunction</a>?</i>" The other extremal solution is the <a href="/facts/Eilenberg%E2%80%93Moore_category/6fX10Qrx">Eilenberg–Moore category</a>. Kleisli categories are named for the mathematician <a href="/facts/Heinrich_Kleisli/mJK1LNNt">Heinrich Kleisli</a>. </p>