nLab categorical algebra -- contents

category theory+algebra

internalization and categorical algebra

• monoid object

• group object

• ring object

• algebra object (associative, Lie, …)

• module object/action object

• internal locale

• internal category ($\to$ more)

  • internal groupoid

  • internal site

  • internal diagram

universal algebra

• algebras over$\,$ algebraic theories

• algebras over$\,$ monads

• algebras over$\,$ operads

categorical semantics

• internal logic, internal language

• relation between category theory and type theory