{"name": "*Aut", "objects_hr": "star-autonomous categories", "arrows_hr": "lax monoidal functors"}
{"name": "1", "objects_hr": "(is) the point", "arrows_hr": "(is) the identity arrow"}
{"name": "1Type", "objects_hr": "homotopy 1-types", "arrows_hr": "continuous maps"}
{"name": "2", "objects_hr": "two objects", "arrows_hr": "the walking arrow (and two identity arrows)"}
{"name": "2Cat", "objects_hr": "2-categories", "arrows_hr": "2-functors"}
{"name": "Ab", "objects_hr": "Abelian groups", "arrows_hr": "group maps"}
{"name": "AbCat", "objects_hr": "Abelian categories", "arrows_hr": "right exact functors"}
{"name": "AbTor", "objects_hr": "Abelian torsion groups", "arrows_hr": "group maps"}
{"name": "AbTorF", "objects_hr": "torsion-free Abelian groups", "arrows_hr": "group maps"}
{"name": "AdicCRing", "objects_hr": "commutative adic rings", "arrows_hr": "continuous ring maps"}
{"name": "AdicRing", "objects_hr": "adic rings", "arrows_hr": "continuous ring maps"}
{"name": "AdmRep", "objects_hr": "admissible domain representations", "arrows_hr": "representable continuous maps"}
{"name": "Alg(Ab)", "objects_hr": "algebras of monoids in Ab (rings)", "arrows_hr": "algebra maps"}
{"name": "Ass", "objects_hr": "assemblies", "arrows_hr": "computable maps"}
{"name": "Aut", "objects_hr": "regular (Moore) automata", "arrows_hr": "simulations"}
{"name": "BanAlg", "objects_hr": "Banach algebras", "arrows_hr": "short linear maps"}
{"name": "BanRing", "objects_hr": "Banach rings", "arrows_hr": "short group maps"}
{"name": "Ban_k", "objects_hr": "Banach spaces over fields k", "arrows_hr": "short linear maps"}
{"name": "BiCat", "objects_hr": "bicategories", "arrows_hr": "pseudofunctors"}
{"name": "Bij", "objects_hr": "sets", "arrows_hr": "bijections"}
{"name": "Bimod(Ab)", "objects_hr": "monoids in Ab (rings)", "arrows_hr": "bimodules of monoids in Ab (rings)"}
{"name": "BoolAlg", "objects_hr": "Boolean algebras", "arrows_hr": "lattice maps"}
{"name": "BrMonCat", "objects_hr": "braided monoidal categories", "arrows_hr": "lax monoidal functors"}
{"name": "CMon", "objects_hr": "commutative monoids", "arrows_hr": "monoid maps"}
{"name": "CPO", "objects_hr": "complete partial orders", "arrows_hr": "Scott-continuous maps"}
{"name": "CPROP", "objects_hr": "colored monoidal product & permutation categories", "arrows_hr": "eso strict monoidal functors"}
{"name": "CRing", "objects_hr": "commutative rings", "arrows_hr": "ring maps"}
{"name": "CW", "objects_hr": "CW complexes", "arrows_hr": "cellular maps"}
{"name": "CartSp", "objects_hr": "Cartesian spaces", "arrows_hr": "smooth maps"}
{"name": "Cat", "objects_hr": "categories", "arrows_hr": "functors"}
{"name": "Ch.(Vect_k)", "objects_hr": "chain complices of vector spaces", "arrows_hr": "linear maps"}
{"name": "Circ", "objects_hr": "the natural numbers", "arrows_hr": "Boolean circuits"}
{"name": "Cluster", "objects_hr": "partitioned sets", "arrows_hr": "non-refinement-increasing maps"}
{"name": "CommAlg(Ab)", "objects_hr": "commutative algebras of monoids in Ab (rings)", "arrows_hr": "algebra maps"}
{"name": "Comp", "objects_hr": "compacta (compact Hausdorff spaces)", "arrows_hr": "continuous maps"}
{"name": "CompBoolAlg", "objects_hr": "complete Boolean algebras (CABAs)", "arrows_hr": "lattice maps"}
{"name": "CompCat", "objects_hr": "compact closed categories", "arrows_hr": "lax monoidal functors"}
{"name": "CompLat", "objects_hr": "complete lattices", "arrows_hr": "lattice maps"}
{"name": "CompMet", "objects_hr": "complete metric spaces", "arrows_hr": "short maps"}
{"name": "CompNormGrp", "objects_hr": "complete normed groups", "arrows_hr": "short group maps"}
{"name": "DCPO", "objects_hr": "directed-complete partial orders", "arrows_hr": "Scott-continuous maps"}
{"name": "DGCAlg", "objects_hr": "differential-graded commutative algebras of vector spaces", "arrows_hr": "differential-graded algebra maps"}
{"name": "DGph", "objects_hr": "digraphs", "arrows_hr": "digraph maps"}
{"name": "DSet", "objects_hr": "dendroidal sets", "arrows_hr": "dendroidal maps"}
{"name": "DagCat", "objects_hr": "\u2020-categories (dagger categories)", "arrows_hr": "\u2020-functors (dagger functors)"}
{"name": "DagCompCat", "objects_hr": "compact closed \u2020-categories", "arrows_hr": "lax monoidal \u2020-functors"}
{"name": "DblCat", "objects_hr": "double categories", "arrows_hr": "double functors"}
{"name": "Diff", "objects_hr": "differentiable manifolds", "arrows_hr": "continuous maps"}
{"name": "DirGph", "objects_hr": "directed graphs", "arrows_hr": "graph maps"}
{"name": "DistLat", "objects_hr": "distributive lattices", "arrows_hr": "lattice maps"}
{"name": "Eff", "objects_hr": "sets with computable equality", "arrows_hr": "computable maps"}
{"name": "EffAdmRep", "objects_hr": "effective admissible domain representations", "arrows_hr": "computable continuous maps"}
{"name": "Feyn", "objects_hr": "Feynman diagrams", "arrows_hr": "symmetries of Feynman diagrams"}
{"name": "Field", "objects_hr": "fields", "arrows_hr": "field maps"}
{"name": "FinGrp", "objects_hr": "finite groups", "arrows_hr": "group maps"}
{"name": "FinHilb", "objects_hr": "finite-dimensional Hilbert spaces", "arrows_hr": "short linear maps"}
{"name": "FinMet", "objects_hr": "finite metric spaces", "arrows_hr": "short maps"}
{"name": "FinOrd", "objects_hr": "the finite ordinal numbers", "arrows_hr": "order-preserving maps"}
{"name": "FinSet", "objects_hr": "finite sets", "arrows_hr": "finite maps"}
{"name": "FinVect_k", "objects_hr": "finite vector spaces over fields k", "arrows_hr": "linear maps"}
{"name": "FinVect_q", "objects_hr": "finite vector spaces over finite fields of order q", "arrows_hr": "linear maps"}
{"name": "Frm", "objects_hr": "frames", "arrows_hr": "frame maps"}
{"name": "G", "objects_hr": "the natural numbers", "arrows_hr": "globe maps"}
{"name": "Gph", "objects_hr": "undirected graphs", "arrows_hr": "graph maps"}
{"name": "Grp", "objects_hr": "groups", "arrows_hr": "group maps"}
{"name": "Grpd", "objects_hr": "groupoids", "arrows_hr": "functors"}
{"name": "Haus", "objects_hr": "Hausdorff (T\u2082) spaces", "arrows_hr": "continuous maps"}
{"name": "HeytAlg", "objects_hr": "Heyting algebras", "arrows_hr": "lattice maps"}
{"name": "Hilb", "objects_hr": "Hilbert spaces", "arrows_hr": "short linear maps"}
{"name": "Hilb\u2080", "objects_hr": "Hilbert spaces", "arrows_hr": "unitary operators"}
{"name": "Ho(Cat)", "objects_hr": "categories", "arrows_hr": "natural isomorphism classes of functors"}
{"name": "Ho(Eff)", "objects_hr": "numbered sets", "arrows_hr": "homotopy classes of computable maps"}
{"name": "Ho(Grpd)", "objects_hr": "groupoids", "arrows_hr": "natural isomorphism classes of functors"}
{"name": "Ho(Top)", "objects_hr": "topological spaces", "arrows_hr": "homotopy classes of continuous maps"}
{"name": "Hyp", "objects_hr": "finite directed hypergraphs", "arrows_hr": "hypergraph maps"}
{"name": "I", "objects_hr": "two objects", "arrows_hr": "the walking isomorphism (and two identity arrows)"}
{"name": "Idem", "objects_hr": "idempotent endofunctions", "arrows_hr": "idempotency-respecting maps"}
{"name": "Inj", "objects_hr": "sets", "arrows_hr": "injections"}
{"name": "KV", "objects_hr": "computable real numbers", "arrows_hr": "computable maps"}
{"name": "LMet", "objects_hr": "Lawvere metric spaces", "arrows_hr": "short maps"}
{"name": "Lat", "objects_hr": "lattices", "arrows_hr": "lattice maps"}
{"name": "Lex", "objects_hr": "finitely complete categories", "arrows_hr": "left exact functors"}
{"name": "LieAlg_k", "objects_hr": "Lie algebras over vector spaces over fields k", "arrows_hr": "linear maps"}
{"name": "LieGrp", "objects_hr": "Lie groups", "arrows_hr": "smooth group maps"}
{"name": "LieRing", "objects_hr": "Lie rings", "arrows_hr": "group maps"}
{"name": "Loc", "objects_hr": "locales", "arrows_hr": "continuous maps"}
{"name": "Log", "objects_hr": "topoi", "arrows_hr": "logical functors"}
{"name": "Man", "objects_hr": "smooth manifolds", "arrows_hr": "smooth maps"}
{"name": "Mat_R", "objects_hr": "the natural numbers", "arrows_hr": "matrices over rings R"}
{"name": "Mat_SR", "objects_hr": "the natural numbers", "arrows_hr": "matrices over semirings SR"}
{"name": "Mat_k", "objects_hr": "the natural numbers", "arrows_hr": "matrices over fields k"}
{"name": "Meas", "objects_hr": "measurable spaces", "arrows_hr": "measurable maps"}
{"name": "Met", "objects_hr": "metric spaces", "arrows_hr": "short maps"}
{"name": "Mod(Ab)", "objects_hr": "modules of monoids in Ab (rings)", "arrows_hr": "module maps"}
{"name": "Mon", "objects_hr": "monoids", "arrows_hr": "monoid maps"}
{"name": "MonCat", "objects_hr": "monoidal categories", "arrows_hr": "lax monoidal functors"}
{"name": "Mono", "objects_hr": "injections", "arrows_hr": "commuting squares"}
{"name": "MultiSet", "objects_hr": "multisets", "arrows_hr": "multimaps"}
{"name": "NormAb", "objects_hr": "normed Abelian groups", "arrows_hr": "group maps"}
{"name": "NormGrp", "objects_hr": "normed groups", "arrows_hr": "short group maps"}