Handbook of Categorical Algebra 2: Categories and Structures, Volume 2

a-filtered colimits a-presentable abelian category abelian groups additive functor adjunction algebraic theory arrow axiom bidense bijections biproducts canonical cartesian functor cartesian morphism choose closure operation cocomplete cocone coequalizer Coker cokernel colim commutative compact composite cone consider diagram construction coproducts corresponding D₁ define definition elements equivalence relation exact sequence exists F preserves fibration fibration F fibre filtered colimits finite limits forgetful functor full subcategory functor F image factorization implies isomorphism kernel pair left adjoint Let F mapping monad monoidal closed category monomorphism morphism f natural transformation notation observe obvious phism pointwise preserves finite Proof Proposition pseudo-elements pullback R-module regular cardinal regular category regular epimorphism remains to prove representable functor right adjoint small category subobjects subset suffices to prove symmetric monoidal closed T-algebras T-model theorem topology torsion theory unique morphism volume yields Yoneda lemma zero object