Handbook of Categorical Algebra: Volume 1, Basic Category Theory
Cambridge University Press, 26 ago. 1994 - 345 páginas
The Handbook of Categorical Algebra is designed to give, in three volumes, a detailed account of what should be known by everybody working in, or using, category theory. As such it will be a unique reference. The volumes are written in sequence, with the first being essentially self-contained, and are accessible to graduate students with a good background in mathematics. In particular, Volume 1, which is devoted to general concepts, can be used for advanced undergraduate courses on category theory.
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2-category 2-cells 2-functor A G M abelian groups adjoint functor Ai>B arrow f axiom bicategory bidense morphisms bijection canonical morphisms category of sets category Q Cauchy complete choose cocomplete cocone coequalizer colim commutative composition law conditions are equivalent cone Consider a category Consider a ﬁnitely Consider a functor consider diagram continuous mappings contravariant coproduct corresponding deﬁned deﬁnition dense distributors equality equivalence relation exists a unique f o g ﬁltered colimits ﬁnd ﬁnite limits ﬁnitely complete category ﬁrst ﬁxed ﬂat functor following conditions full and faithful functor F given group homomorphism injective internal category inverted isomorphism Kan extension kernel pair left adjoint left exact modiﬁcations monomorphism morphism f natural transformation notation notion object C G phism preserves Proposition pullback quotient reﬂective subcategory representable functor right adjoint satisﬁes small category strong epimorphism subobject surjective theorem topological spaces unique factorization unique morphism universal closure operation Yoneda embedding