List of category-theory notes:

• Inclusion subcategory
• Injective object
• Category of categories
• Types of morphisms
• Comma category
• Opposite category
• Casting in categories
• Hom-set
• Group action
• Slice categories
• Functors
• Definition of a category
• Category of models
• Category of fields
• Full and faithful functors
• Categories of graphs
• Category-homotopy analogy
• Equivalence of categories
• Conditions for finite completeness
• Subobject classifier
• Representable functor
• Functor category
• Natural transformations between representable functors
• Cones and limits
• Pushout and pullback
• Complete category
• Subobject
• The Yoneda lemma
• Diagonal functor
• Coproduct
• Coequalizer
• Universal arrow
• Yoneda Functor
• Morphisms between linear orders
• Monoidal category
• Kernels and zero arrows
• Reflective subcategory
• Exact sequence
• Monoid in a category
• Preorder
• Closure operator
• Categories with finite colimits
• Elementary topos
• Sieve
• Adjunction
• Truth values in a topos
• Internal hom
• Galois connection
• Skeleton category
• Sheaf of germs
• Sheaf
• Inverse image self-adjunction
• Inclusion-forgetful adjunction to a comma category
• Consequences of a subobject classifier
• Discrete-forgetful-indiscrete adjunction between Top and Set
• Monad
• Free-forgetful adjunction from Grp to Set
• Heyting algebra
• Spatial topos
• Comma category of a topos
• Algebraic system