This is a small diagram I put together using the wonderful GraphViz . The nodes in this graph denote categories of object, while an arrow $A \to B$ denotes some kind of "inclusion" of categories.

(More precisely, it denotes the existence of a forgetful functor from $B$ to $A$ , so perhaps I should reverse the arrows!)

G
Sets
Sets
Magmas
Magmas
Sets->Magmas
Posets
Posets
Sets->Posets
Topological Spaces
Topological Spaces
Sets->Topological Spaces
Measurable Spaces
Measurable Spaces
Sets->Measurable Spaces
Semigroups
Semigroups
Magmas->Semigroups
Quasigroups
Quasigroups
Magmas->Quasigroups
Lattices
Lattices
Posets->Lattices
Metric Spaces
Metric Spaces
Topological Spaces->Metric Spaces
Manifolds
Manifolds
Topological Spaces->Manifolds
Normed Spaces
Normed Spaces
Topological Spaces->Normed Spaces
Measure Spaces
Measure Spaces
Topological Spaces->Measure Spaces
Topological Groups
Topological Groups
Topological Spaces->Topological Groups
Topological Vector Spaces
Topological Vector Spaces
Topological Spaces->Topological Vector Spaces
Monoids
Monoids
Semigroups->Monoids
Loops
Loops
Quasigroups->Loops
Groups
Groups
Loops->Groups
Abelian Groups
Abelian Groups
Groups->Abelian Groups
Groups->Topological Groups
Lie Groups
Lie Groups
Groups->Lie Groups
Monoids->Groups
Rings
Rings
Monoids->Rings
Abelian Groups->Rings
Modules
Modules
Abelian Groups->Modules
Vector Spaces
Vector Spaces
Abelian Groups->Vector Spaces
Integral Domains
Integral Domains
Rings->Integral Domains
Rings->Modules
Algebras
Algebras
Rings->Algebras
UFDs
UFDs
Integral Domains->UFDs
PIDs
PIDs
UFDs->PIDs
Euclidean Domains
Euclidean Domains
PIDs->Euclidean Domains
Fields
Fields
Euclidean Domains->Fields
Fields->Vector Spaces
Fields->Algebras
Modules->Vector Spaces
Vector Spaces->Algebras
Vector Spaces->Normed Spaces
Vector Spaces->Topological Vector Spaces
Tensor Algebras
Tensor Algebras
Algebras->Tensor Algebras
Lie Algebras
Lie Algebras
Algebras->Lie Algebras
Clifford Algebras
Clifford Algebras
Tensor Algebras->Clifford Algebras
Exterior Algebras
Exterior Algebras
Tensor Algebras->Exterior Algebras
Geometric Algebras
Geometric Algebras
Clifford Algebras->Geometric Algebras
Metric Spaces->Manifolds
Riemannian Manifolds
Riemannian Manifolds
Metric Spaces->Riemannian Manifolds
Manifolds->Riemannian Manifolds
Manifolds->Lie Groups
Banach Spaces
Banach Spaces
Normed Spaces->Banach Spaces
Inner Product Spaces
Inner Product Spaces
Normed Spaces->Inner Product Spaces
Hilbert Spaces
Hilbert Spaces
Inner Product Spaces->Hilbert Spaces
Measurable Spaces->Measure Spaces
Measure Spaces->Normed Spaces
Probability Spaces
Probability Spaces
Measure Spaces->Probability Spaces
Lie Groups->Lie Algebras

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