| Equivariant points give homotopy fixed points | statement | lemma 3.28 | arxiv |
| Pointed mapping objects and reduced objects | statement | corollary 3.23 | arxiv |
| Equivariant identification of the reduced object | statement | lemma 3.27 | arxiv |
| $n$-connected cover | definition | definition A.15 | arxiv |
| Fibration theorem for magnetic symmetries | statement | theorem 3.15 | arxiv |
| Factorization theorem for higher Pontryagin magnetic symmetries | statement | theorem 4.1 | arxiv |
| Category of spectrum objects | definition | definition A.23 | arxiv |
| Pure discrete gauge theory | statement | corollary 4.12 | arxiv |
| $\infty$-Mapping class group | definition | definition 2.15 | arxiv |
| Symmetries induced by a trivially-co-acting magnetic co-symmetry | example | example 3.10 | arxiv |
| 3P64N3FDT6 | statement | lemma 4.2 | arxiv |
| Electric $\Z_2$-action on magnetic charges for $\X=S^1$ | example | example 2.18 | arxiv |
| Trivially-co-acting magnetic co-symmetry | definition | definition 2.13 | arxiv |
| 5A6CY3BWW9 | statement | proposition 4.26 | arxiv |
| Co-)slice categories | definition | definition A.2 | arxiv |
| Domain splitting | statement | lemma 4.4 | arxiv |
| External and internal hom-objects | definition | definition A.1 | arxiv |
| 67BBRJP71K | definition | definition | arxiv |
| Magnetic charges as the shape of fields | statement | proposition 2.5 | arxiv |
| Simplicial and co-simplicial objects | definition | definition A.5 | arxiv |
| Homotopy fixed points of the reduced sequence | statement | lemma 3.25 | arxiv |
| A8HWNSXNJC | statement | proposition 4.27 | arxiv |
| Magnetic $\T$-symmetry backgrounds | definition | definition 3.3 | arxiv |
| Stable versus connective homotopy fixed points | statement | lemma 3.30 | arxiv |
| $n$-connected object | definition | definition A.14 | arxiv |
| Shape of the action quotient | statement | lemma 3.16 | arxiv |
| Splitting of the pointed quotient mapping object | statement | lemma 3.29 | arxiv |
| Transfer | statement | lemma 4.25 | arxiv |
| The equivariant reduced fiber sequence | statement | lemma 3.24 | arxiv |
| E4QH5W78AG | statement | corollary 4.21 | arxiv |
| Cohesive structure on \textbf{H | definition | definition A.17 | arxiv |
| $n$-truncated and $n$-connected morphism | definition | definition A.16 | arxiv |
| Softness (e.g. | statement | lemma 4.8 | arxiv |
| Co-)slice categories of the terminal object and pointed stacks | example | example A.3 | arxiv |
| Electric symmetries act on magnetic charges | statement | corollary 2.17 | arxiv |
| Homotopy quotients of group actions in $\textbf{H}$ | definition | definition A.11 | arxiv |
| Terminal groupoid object | example | example A.7 | arxiv |
| Co)unit-induced equivalences | statement | proposition A.20 | arxiv |
| Group actions in $\textbf{H}$ | definition | definition A.10 | arxiv |
| Stable homotopy-fixed-point spectral sequence | statement | lemma 3.31 | arxiv |
| Consistency checks | example | example 3.35 | arxiv |
| $\mathrm{t}$-structure | definition | definition A.26 | arxiv |
| JME4SZCNEC | statement | lemma 4.19 | arxiv |
| Connecting map | statement | lemma 4.22 | arxiv |
| Classical Dold--Kan correspondence | definition | definition A.31 | arxiv |
| JZJDKF725T | definition | definition 3.20 | arxiv |
| KV8BN7JAY5 | statement | lemma B.1 | arxiv |
| Simplex category | definition | definition A.4 | arxiv |
| Postnikov magnetic co-symmetries | definition | definition 2.12 | arxiv |
| Magnetic charges | definition | definition 2.4 | arxiv |
| Mapping out of a colimit | statement | lemma 3.17 | arxiv |
| Nonnegative-degree abutment | statement | corollary 3.32 | arxiv |
| Splitting for objectwise Dold--Kan targets | statement | proposition 4.7 | arxiv |
| $n$-truncated smooth stack | definition | definition A.13 | arxiv |
| Additive Deligne complex (cf. | statement | lemma 4.9 | arxiv |
| Connectivity of the splitting | statement | lemma 3.22 | arxiv |
| Discrete object | definition | definition A.18 | arxiv |
| Retracts of stacks are stacks | statement | lemma 4.6 | arxiv |
| Passage to pointed mapping objects | statement | lemma 3.26 | arxiv |
| $n$-truncation of stacks | definition | definition A.12 | arxiv |
| $S^1$-valued $\sigma$-models | example | example 4.17 | arxiv |
| Splitting of a retraction in a stable category | statement | lemma 3.21 | arxiv |
| T9M3DWZC5B | statement | lemma B.2 | arxiv |
| Stable $\infty$-category | definition | definition A.22 | arxiv |
| Connective spectra | definition | definition A.29 | arxiv |
| Points-to-pieces transform | definition | definition A.21 | arxiv |
| Magnetic charges of the circle | example | example 2.7 | arxiv |
| Truncation functors | definition | definition A.28 | arxiv |
| Groupoid object in $\textbf{H}$ | definition | definition A.6 | arxiv |
| Magnetic charges of Maxwell theory | example | example 2.8 | arxiv |
| Finite $1$-group gauge theory | example | example 4.13 | arxiv |
| Group object in $\textbf{H}$ | definition | definition A.8 | arxiv |
| ZRK9TF1APW | statement | lemma 4.20 | arxiv |
| Pointed version | statement | corollary 4.3 | arxiv |
