{"name": "DagCat", "objects_hr": "\u2020-categories (dagger categories)", "arrows_hr": "\u2020-functors (dagger functors)"}
{"name": "Vect_k", "objects_hr": "vector spaces over fields k", "arrows_hr": "linear maps"}
{"name": "Gph", "objects_hr": "undirected graphs", "arrows_hr": "graph maps"}
{"name": "2", "objects_hr": "two objects", "arrows_hr": "the walking arrow (and two identity arrows)"}
{"name": "I", "objects_hr": "two objects", "arrows_hr": "the walking isomorphism (and two identity arrows)"}
{"name": "TracedSymmMonCat", "objects_hr": "traced symmetric monoidal categories", "arrows_hr": "lax monoidal functors"}
{"name": "AbTorF", "objects_hr": "torsion-free Abelian groups", "arrows_hr": "group maps"}
{"name": "TopCat", "objects_hr": "topologically enriched categories", "arrows_hr": "continuous functors"}
{"name": "TopVect", "objects_hr": "topological vector spaces", "arrows_hr": "linear maps"}
{"name": "Spectra", "objects_hr": "topological spectra", "arrows_hr": "spectrum maps"}
{"name": "Ho(Top)", "objects_hr": "topological spaces", "arrows_hr": "homotopy classes of continuous maps"}
{"name": "Top", "objects_hr": "topological spaces", "arrows_hr": "continuous maps"}
{"name": "TopRing", "objects_hr": "topological rings", "arrows_hr": "continuous ring maps"}
{"name": "TopMon", "objects_hr": "topological monoids", "arrows_hr": "continuous monoid maps"}
{"name": "TopMan", "objects_hr": "topological manifolds", "arrows_hr": "continuous maps"}
{"name": "TopGrp", "objects_hr": "topological groups", "arrows_hr": "continuous group maps"}
{"name": "Topos", "objects_hr": "topoi", "arrows_hr": "geometric arrows"}
{"name": "Log", "objects_hr": "topoi", "arrows_hr": "logical functors"}
{"name": "Mat_SR", "objects_hr": "the natural numbers", "arrows_hr": "matrices over semirings SR"}
{"name": "Circ", "objects_hr": "the natural numbers", "arrows_hr": "Boolean circuits"}
{"name": "RT(K\u2081)", "objects_hr": "the natural numbers", "arrows_hr": "partial realizable maps"}
{"name": "Mat_k", "objects_hr": "the natural numbers", "arrows_hr": "matrices over fields k"}
{"name": "G", "objects_hr": "the natural numbers", "arrows_hr": "globe maps"}
{"name": "Mat_R", "objects_hr": "the natural numbers", "arrows_hr": "matrices over rings R"}
{"name": "Perm", "objects_hr": "the natural numbers", "arrows_hr": "permutations"}
{"name": "\u03a9", "objects_hr": "the inhabited trees", "arrows_hr": "tree maps"}
{"name": "\u0394", "objects_hr": "the inhabited simplices", "arrows_hr": "monotone maps"}
{"name": "\u25a1", "objects_hr": "the inhabited cubes", "arrows_hr": "cubical maps"}
{"name": "FinOrd", "objects_hr": "the finite ordinal numbers", "arrows_hr": "order-preserving maps"}
{"name": "Operad", "objects_hr": "symmetric multicategories", "arrows_hr": "multifunctors"}
{"name": "SymCat", "objects_hr": "symmetric monoidal categories", "arrows_hr": "lax monoidal functors"}
{"name": "SymmMonCat", "objects_hr": "symmetric monoidal categories", "arrows_hr": "lax monoidal functors"}
{"name": "SymLMet", "objects_hr": "symmetric Lawvere metric spaces", "arrows_hr": "short maps"}
{"name": "SupLat", "objects_hr": "suplattices", "arrows_hr": "suplattice maps"}
{"name": "SupVect_k", "objects_hr": "super vector spaces over fields k", "arrows_hr": "super linear maps"}
{"name": "Ste", "objects_hr": "stereotype spaces", "arrows_hr": "continuous maps"}
{"name": "*Aut", "objects_hr": "star-autonomous categories", "arrows_hr": "lax monoidal functors"}
{"name": "Species", "objects_hr": "species", "arrows_hr": "natural transformations"}
{"name": "SpLoc", "objects_hr": "spatial locales", "arrows_hr": "continuous maps"}
{"name": "SoberTop", "objects_hr": "sober topological spaces", "arrows_hr": "continuous maps"}
{"name": "Poiss", "objects_hr": "smooth manifolds with Poisson structures", "arrows_hr": "Poisson maps"}
{"name": "Man", "objects_hr": "smooth manifolds", "arrows_hr": "smooth maps"}
{"name": "SimpCat", "objects_hr": "simplicially enriched categories", "arrows_hr": "simplicially enriched functors"}
{"name": "STop", "objects_hr": "simplicial topological spaces", "arrows_hr": "continuous maps"}
{"name": "STopGrp", "objects_hr": "simplicial topological groups", "arrows_hr": "continuous group maps"}
{"name": "SMan", "objects_hr": "simplicial smooth manifolds", "arrows_hr": "smooth maps"}
{"name": "SSet", "objects_hr": "simplicial sets", "arrows_hr": "simplicial maps"}
{"name": "SRing", "objects_hr": "simplicial rings", "arrows_hr": "ring maps"}
{"name": "SGrp", "objects_hr": "simplicial groups", "arrows_hr": "group maps"}
{"name": "SLieAlg_k", "objects_hr": "simplicial Lie algebras over vector spaces over fields k", "arrows_hr": "linear maps"}
{"name": "SAb", "objects_hr": "simplicial Abelian groups", "arrows_hr": "group maps"}
{"name": "SES(Ab)", "objects_hr": "short exact sequences of Abelian groups", "arrows_hr": "commuting diagrams"}
{"name": "Eff", "objects_hr": "sets with computable equality", "arrows_hr": "computable maps"}
{"name": "Bij", "objects_hr": "sets", "arrows_hr": "bijections"}
{"name": "Rel", "objects_hr": "sets", "arrows_hr": "relations"}
{"name": "Set", "objects_hr": "sets", "arrows_hr": "maps"}
{"name": "Span(Set)", "objects_hr": "sets", "arrows_hr": "spans of functions"}
{"name": "Pfn", "objects_hr": "sets", "arrows_hr": "partial maps"}
{"name": "Inj", "objects_hr": "sets", "arrows_hr": "injections"}
{"name": "Surj", "objects_hr": "sets", "arrows_hr": "surjections"}
{"name": "SymmRel", "objects_hr": "sets", "arrows_hr": "symmetric relations"}
{"name": "RT(K\u2082)", "objects_hr": "sequences of natural numbers", "arrows_hr": "partial realizable maps"}
{"name": "SemiRing", "objects_hr": "semirings (rigs)", "arrows_hr": "semiring maps"}
{"name": "SemiLat", "objects_hr": "semilattices", "arrows_hr": "semilattice maps"}
{"name": "SemiGrp", "objects_hr": "semigroups", "arrows_hr": "semigroup maps"}
{"name": "Ring", "objects_hr": "rings", "arrows_hr": "ring maps"}
{"name": "RCat", "objects_hr": "restriction categories", "arrows_hr": "functors"}
{"name": "Aut", "objects_hr": "regular (Moore) automata", "arrows_hr": "simulations"}
{"name": "Quiv", "objects_hr": "quivers", "arrows_hr": "graph maps"}
{"name": "Quant", "objects_hr": "quantales", "arrows_hr": "suplattice maps"}
{"name": "PseudoMet", "objects_hr": "pseudometric spaces", "arrows_hr": "short maps"}
{"name": "PreOrd", "objects_hr": "preorders", "arrows_hr": "monotone maps"}
{"name": "Pros", "objects_hr": "preorders", "arrows_hr": "monotone maps"}
{"name": "Top*", "objects_hr": "pointed topological spaces", "arrows_hr": "based continuous maps"}
{"name": "Set*", "objects_hr": "pointed sets", "arrows_hr": "based maps"}
{"name": "PL", "objects_hr": "piecewise-linear manifolds", "arrows_hr": "piecewise-continuous maps"}
{"name": "PDiff", "objects_hr": "piecewise-differentiable manifolds", "arrows_hr": "piecewise-continuous maps"}
{"name": "PermCat", "objects_hr": "permutative (symmetric strict monoidal) categories", "arrows_hr": "multilinear functors"}
{"name": "Cluster", "objects_hr": "partitioned sets", "arrows_hr": "non-refinement-increasing maps"}
{"name": "Pos", "objects_hr": "partial orders", "arrows_hr": "monotone maps"}
{"name": "Op(FinCartSp)", "objects_hr": "open sets of finite-dimensional Cartesian spaces", "arrows_hr": "inclusions"}
{"name": "Ho(Eff)", "objects_hr": "numbered sets", "arrows_hr": "homotopy classes of computable maps"}
{"name": "NormGrp", "objects_hr": "normed groups", "arrows_hr": "short group maps"}
{"name": "NormAb", "objects_hr": "normed Abelian groups", "arrows_hr": "group maps"}
{"name": "NormRing", "objects_hr": "normed (commutative) rings", "arrows_hr": "short group maps"}
{"name": "Rng", "objects_hr": "nonunital rings", "arrows_hr": "nonunital ring maps"}
{"name": "R+", "objects_hr": "non-negative real numbers", "arrows_hr": "addition"}
{"name": "MultiSet", "objects_hr": "multisets", "arrows_hr": "multimaps"}
{"name": "Bimod(Ab)", "objects_hr": "monoids in Ab (rings)", "arrows_hr": "bimodules of monoids in Ab (rings)"}
{"name": "Mon", "objects_hr": "monoids", "arrows_hr": "monoid maps"}
{"name": "PROP", "objects_hr": "monoidal product & permutation categories", "arrows_hr": "eso strict monoidal functors"}
{"name": "MonCat", "objects_hr": "monoidal categories", "arrows_hr": "lax monoidal functors"}
{"name": "Mod(Ab)", "objects_hr": "modules of monoids in Ab (rings)", "arrows_hr": "module maps"}
{"name": "Met", "objects_hr": "metric spaces", "arrows_hr": "short maps"}
{"name": "Meas", "objects_hr": "measurable spaces", "arrows_hr": "measurable maps"}
{"name": "Sierp", "objects_hr": "maps", "arrows_hr": "commuting squares"}
{"name": "PrCat", "objects_hr": "locally presentable categories", "arrows_hr": "left adjoint functors"}
{"name": "Loc", "objects_hr": "locales", "arrows_hr": "continuous maps"}
{"name": "Lat", "objects_hr": "lattices", "arrows_hr": "lattice maps"}
{"name": "Mono", "objects_hr": "injections", "arrows_hr": "commuting squares"}