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Geometric Realization of Simplicial Sets
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1-morphism 2-category abelian category adjunction morphism admits a calculus amalgamated sum anodyne extension base point bijection calculus of left canonical functor canonical morphism canonical projection category of fractions cokernel commutative diagram commutative diagram Fig commutative square commutes with direct commutes with finite connected components continuous map defined denotes diagram scheme direct limits direct sum domain epimorphism exact sequence fibred product follows full subcategory fully faithful functor F geometric realization functor groupoid Hence homeomorphism homology identified inclusion injection inverse limits invertible Kelley space left adjoint left fractions lemma minimal fibration modulo homotopy monomorphism Moreover morphism f notations obviously Poincare group pointed complex pointed groupoids pointed homotopic category pointed Kan complex pointed topological spaces proposition prove quotient resp right adjoint satisfies conditions set of morphisms simplicial set simply singular simplex square of Fig subcomplex subset surjection theorem write X-+Y zero morphism