Notes on Categories and Groupoids |
Contents
Some basic categories | 1 |
Natural equivalence and adjoint functors | 21 |
Paths and components | 23 |
Copyright | |
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Common terms and phrases
a₁ a₂ adjoint pair algebraic b₁ b₂ canonical map category or groupoid category-map cohomology commutative component construction coproduct COROLLARY corresponding cosets covering map D-diagram defined denote diagram difference cokernel disjoint union edges face-maps finite follows forgetful functor free category free group free groupoid free product full subgroupoid fundamental group G₁ graph graph-map groupoid G H₁ Hence homology groups homomorphisms homotopy identity elements identity map inclusion map induced cover induced map injection isomorphic kernel left adjoint left limits lemma n-simplex natural equivalence natural transformation normal subgroupoid objects path of length Proof Proposition prove pull-back push-out quotient map reduced paths representation retraction simplicial groupoid spans subgroup Suppose surjective T₁ Theorem 13 theory unicursal unique universal morphism universal property vertex group vertex map vertex set vertices word problem y₁ Χλμ