| 1SMCMEYHTP | statement | proposition 4.14 | arxiv |
| Topological dictionary | statement | proposition 4.19 | arxiv |
| 24JHZPFTQ6 | statement | proposition 4.7 | arxiv |
| 2825T1NQS0 | statement | corollary 4.28 | arxiv |
| A nonconservative Grandis transfer functor | counterexample | counterexample 3.18 | arxiv |
| 2DJRKRK9VC | statement | proposition 4.25 | arxiv |
| 2N9GY374ZM | statement | lemma 3.3 | arxiv |
| 2Q3MDC3GZG | statement | corollary 4.27 | arxiv |
| 334256CSH9 | statement | corollary 4.44 | arxiv |
| 3HV3X915JZ | problem | problem 4.55 | arxiv |
| 3KR1AGVH5Z | statement | proposition 3.39 | arxiv |
| Recovering a form with modular fibres | statement | proposition 3.16 | arxiv |
| Grandis transfer functors | statement | corollary 3.17 | arxiv |
| 49ERNAFXDH | statement | lemma 4.4 | arxiv |
| A necessary size condition | statement | proposition 4.53 | arxiv |
| 4QE3X7HX7J | statement | corollary 4.29 | arxiv |
| Intervals and equality under transport | statement | lemma 2.2 | arxiv |
| 5CKNSV7GBC | statement | corollary 4.49 | arxiv |
| 5S59K6J0ZS | statement | corollary 4.46 | arxiv |
| 5XQNXNK19B | statement | proposition 4.12 | arxiv |
| 6GGX8VTTGB | statement | proposition 4.32 | arxiv |
| 6HAJCPJ2BJ | statement | proposition 4.37 | arxiv |
| Essentially algebraic existence criterion | statement | theorem 3.26 | arxiv |
| Modular lattices as a universal target | statement | corollary 3.25 | arxiv |
| Cluster-set representation | statement | theorem 3.11 | arxiv |
| Rules with at most one premise | statement | theorem 4.35 | arxiv |
| 7MPET2G1YD | statement | proposition 4.23 | arxiv |
| A size obstruction to the natural system | example | example 4.54 | arxiv |
| The canonical form on modular lattices | statement | lemma 3.15 | arxiv |
| 9FN44DF8YR | statement | proposition 4.50 | arxiv |
| A sufficient geometric condition | statement | theorem 3.31 | arxiv |
| A39GC6H5C9 | statement | corollary 4.18 | arxiv |
| A4AD2WFB9C | statement | lemma 3.35 | arxiv |
| A7A4D8802Q | definition | definition 3.1 | arxiv |
| Existence characterization | statement | theorem 3.12 | arxiv |
| AKVZKB43Z7 | counterexample | counterexample 3.40 | arxiv |
| BBSA67NBDZ | statement | corollary 4.42 | arxiv |
| BPMVWCSPPN | statement | proposition 3.37 | arxiv |
| BPRE3DC5E9 | statement | lemma 2.1 | arxiv |
| BRXB7NTD15 | statement | lemma 4.3 | arxiv |
| BWTR8KS308 | statement | proposition 4.6 | arxiv |
| CKVZF50ZY0 | statement | theorem 4.26 | arxiv |
| Free-algebra functors | statement | theorem 3.20 | arxiv |
| D05C1CHMZC | statement | proposition 4.48 | arxiv |
| D6B2QRCJB1 | definition | definition | arxiv |
| DS2G615VDD | statement | lemma 4.5 | arxiv |
| E3DYXGV5NQ | statement | proposition 4.39 | arxiv |
| EE4A8S59J3 | definition | definition 3.14 | arxiv |
| A topological category without these tests | example | example 4.51 | arxiv |
| FNHYHRFQ0W | statement | corollary 4.47 | arxiv |
| G8TW4YJ5NB | statement | corollary 4.30 | arxiv |
| GTDX01NSJ4 | statement | corollary 4.45 | arxiv |
| The concrete quotient dictionary | statement | proposition 4.16 | arxiv |
| H4374YXXDM | statement | proposition 4.13 | arxiv |
| Categories, groupoids, and semicategories | statement | corollary 3.28 | arxiv |
| Inheritance by subobjects and quotients | statement | proposition 3.30 | arxiv |
| JQ76YGMKCF | statement | proposition 3.38 | arxiv |
| Two useful partial equivalences | statement | corollary 3.9 | arxiv |
| Ideally exact categories | statement | theorem 3.36 | arxiv |
| Varieties as universal targets | statement | theorem 3.22 | arxiv |
| MRBG3A4BVZ | statement | proposition 4.9 | arxiv |
| Transfer and necessity | statement | theorem 3.8 | arxiv |
| N0C3XM298E | statement | proposition 4.34 | arxiv |
| Premise variables retained in the conclusion | statement | theorem 4.36 | arxiv |
| NC3FR48TBZ | statement | proposition 3.7 | arxiv |
| NDXE25D8P7 | counterexample | counterexample 3.10 | arxiv |
| NYN65YSNKF | statement | corollary 4.17 | arxiv |
| P0CH7BE9H9 | statement | theorem 4.15 | arxiv |
| PFW4T6RZD2 | statement | corollary 4.20 | arxiv |
| Conservativity forced by (N2 | statement | proposition 3.5 | arxiv |
| Q2YC8RDXG6 | statement | corollary 4.31 | arxiv |
| RGXXHHX5Q4 | statement | proposition 3.2 | arxiv |
| RKDGBET3T1 | statement | proposition 4.11 | arxiv |
| SCKV2HPCJC | statement | corollary 4.43 | arxiv |
| SJ974NY5Z4 | statement | lemma 4.10 | arxiv |
| SRJNWNNRRS | statement | proposition 4.1 | arxiv |
| Modularity imposes no additional existence condition | statement | corollary 3.24 | arxiv |
| T5DJYET189 | statement | proposition 4.8 | arxiv |
| TM92ECADS7 | statement | corollary 4.33 | arxiv |
| The theory of inhabited sets | counterexample | counterexample 3.33 | arxiv |
| The (N2) criterion | statement | theorem 3.4 | arxiv |
| Monadic pullback criterion | statement | theorem 3.34 | arxiv |
| Measurable isomorphism and correspondence rules | statement | corollary 4.24 | arxiv |
| VX4WPPZFWY | definition | definition 4.2 | arxiv |
| Modular-fibre replacement | statement | theorem 3.23 | arxiv |
| WJVEYBYZWK | statement | corollary 4.21 | arxiv |
| The semigroup transfer for small categories | statement | proposition 3.27 | arxiv |
| WM5403SYHE | statement | corollary 4.40 | arxiv |
| WRHW1NPW1E | statement | lemma 2.3 | arxiv |
| X38QEP40AD | example | example 3.32 | arxiv |
| Difunctional relations and injective tests | example | example 4.52 | arxiv |
| Closure of the left-adjoint criterion | statement | proposition 3.29 | arxiv |
| XTAG2R07JZ | statement | corollary 4.38 | arxiv |
| The (N3) criterion | statement | proposition 3.6 | arxiv |
| YFZNTF1K4Z | definition | definition 4.22 | arxiv |
| Underlying-set functors | statement | proposition 3.19 | arxiv |
| Criterion for a universal target | statement | proposition 3.13 | arxiv |
| ZXHWRDCNJN | statement | corollary 4.41 | arxiv |
