category theory
category
functor
natural transformation
Cat
universal construction
representable functor
adjoint functor
limit/colimit
weighted limit
end/coend
Kan extension
Yoneda lemma
Isbell duality
Grothendieck construction
adjoint functor theorem
monadicity theorem
adjoint lifting theorem
Tannaka duality
Gabriel-Ulmer duality
small object argument
Freyd-Mitchell embedding theorem
relation between type theory and category theory
sheaf and topos theory
enriched category theory
higher category theory
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The dual notion of projective presentation.
projective object, projective presentation, projective cover, projective resolution
injective object, injective presentation, injective envelope, injective resolution
free object, free resolution
flat object, flat resolution