Category:Category theory
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branch of mathematics studying categories, functors, and natural transformations  | |||||
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English: Category theory is a mathematical theory that deals in an abstract way with mathematical structures and relationships between them.
Subcategories
This category has the following 11 subcategories, out of 11 total.
C
- Comma categories (11 F)
E
F
H
M
- Module theory (43 F)
- Monoidal category (2 F)
O
Q
- Quivers (graph theory) (8 F)
Pages in category "Category theory"
This category contains only the following page.
Media in category "Category theory"
The following 190 files are in this category, out of 190 total.
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2 point discrete space.png 151 × 137; 1 KB
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AlgebraicGroup diagrams.gif 580 × 189; 4 KB
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Anafunctor (span).pdf 266 × 147; 26 KB
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Anafunctor (span).svg 171 × 96; 10 KB
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Applicative Form of Monoidal Coherence Map 01.svg 516 × 78; 99 KB
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Arrow diagram transitive.png 206 × 77; 1,023 bytes
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Associativity Coherence of Tensorial Strengths.svg 381 × 71; 82 KB
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Baby Category 1 plus 1.svg 187 × 89; 6 KB
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Baby Category 1.svg 77 × 86; 4 KB
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Baby Category 2.svg 187 × 89; 7 KB
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BabyCategory 1.png 74 × 78; 352 bytes
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BabyCategory 1plus1.png 189 × 82; 545 bytes
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BabyCategory 2.png 195 × 91; 582 bytes
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Bialgebra4a.svg 185 × 61; 26 KB
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Braid category hexagon.svg 688 × 188; 28 KB
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Braid category inverse hexagon.svg 688 × 188; 30 KB
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Carré cartésien diagramme.png 570 × 570; 36 KB
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Carré cartésien.png 380 × 380; 16 KB
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Category SVG.svg 150 × 150; 123 KB
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Coker-simple.svg 96 × 55; 18 KB
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Coker-simple2.svg 96 × 55; 18 KB
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Cokernel-thm1.svg 126 × 89; 28 KB
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Cokernel-thm2-1.svg 55 × 53; 16 KB
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Cokernel-thm2-2.svg 55 × 55; 16 KB
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Commutative Diagram 2.jpg 456 × 296; 20 KB
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Composition of morphisms1.jpg 776 × 173; 10 KB
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Composition of Roofs in Derived Category.pdf 1,275 × 1,650, 8 pages; 160 KB
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Compositionoffunctions.png 414 × 235; 12 KB
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Connection between comma category and universal properties.svg 674 × 157; 24 KB
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Connection between universal diagrams and comma categories.svg 674 × 157; 24 KB
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Dagger compact category (diagram).png 193 × 140; 6 KB
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Dagger compact category (diagram).svg 263 × 225; 19 KB
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Dagger Compact Category.svg 500 × 365; 21 KB
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Delta maps.svg 512 × 220; 12 KB
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DeltaFunctorLongExactSequence.png 939 × 475; 34 KB
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Determinant as a natural transformation.svg 161 × 77; 25 KB
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Diag ax cat.gif 500 × 150; 3 KB
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Diagram of geometric categories.png 8,948 × 9,248; 4.36 MB
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Diagram of geometric categories.svg 2,684 × 2,774; 845 KB
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Discrete category.svg 503 × 503; 5 KB
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Distributive law monads mult1.svg 274 × 104; 32 KB
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Distributive law monads mult2.svg 733 × 279; 32 KB
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Distributive law monads unit1.svg 70 × 36; 21 KB
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Distributive law monads unit2.svg 24 × 13; 21 KB
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Eckman hilton clock.svg 679 × 639; 7 KB
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Eckmanhilton.jpg 724 × 682; 40 KB
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Enrichedidentity.png 560 × 173; 16 KB
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Enrichedmult.png 451 × 95; 6 KB
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Enrichment-1.jpg 312 × 235; 7 KB
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Enrichment-2.jpg 547 × 458; 17 KB
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Envelope-1.jpg 206 × 145; 5 KB
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Envelope-2.jpg 266 × 177; 5 KB
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Epimorphism scenarios.svg 340 × 50; 15 KB
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Exact couple.png 241 × 156; 1 KB
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Extension-1.jpg 232 × 163; 5 KB
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Extension-2.jpg 266 × 179; 5 KB
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Extension-3.jpg 252 × 181; 5 KB
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F Algebra Associativity Commutative Diagram.svg 236 × 88; 28 KB
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F Algebra Identity Commutative Diagram.svg 243 × 86; 25 KB
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F Algebra Inverse Commutative Diagram.svg 202 × 86; 24 KB
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Factorisation.svg 85 × 57; 16 KB
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Factorization system functoriality.png 154 × 93; 2 KB
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Factorization system orthogonality.png 92 × 88; 2 KB
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Fibered product detail.svg 300 × 100; 11 KB
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Fibre bundle local trivial.svg 283 × 177; 26 KB
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Free-category-ump.svg 116 × 84; 17 KB
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Free-object-universal-property.svg 319 × 142; 28 KB
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Fullness of a diagonal functor.svg 546 × 327; 26 KB
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FunctionDecompCD.jpg 204 × 147; 11 KB
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Functor Strength By Tensorial Strength.svg 488 × 78; 103 KB
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Functor.png 436 × 243; 45 KB
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Functoriality (2).svg 1,825 × 725; 17 KB
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Functoriality long exact sequence.svg 4,560 × 515; 28 KB
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Functoriality-of-pseudocompletion.jpg 176 × 133; 5 KB
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Functoriality-of-pseudosaturation.jpg 168 × 135; 5 KB
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Functors Between Objects and Morphisms of C.pdf 237 × 122; 4 KB
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Fundamental Homomorphism Theorem v2.svg 92 × 81; 38 KB
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Funtori paralleli kf.png 127 × 89; 2 KB
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Graphical illustration of Hom functor (covariant).svg 765 × 630; 50 KB
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GrothendieckGroupAsFunctor.PNG 187 × 115; 4 KB
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Group associative categories.svg 263 × 125; 15 KB
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Group operation image.tif 258 × 132; 6 KB
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Hochhebungseigenschaft.png 404 × 337; 11 KB
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Hom functor.svg 425 × 213; 30 KB
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Homotopy lifting property.png 200 × 144; 7 KB
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Horizontal composition of natural transformations.svg 1,745 × 440; 24 KB
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Hurewicz2 (corrected).svg 1,416 × 1,006; 20 KB
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Hypermorphisms.pdf 1,275 × 1,650; 57 KB
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Initial and terminal object.png 1,476 × 2,448; 159 KB
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InitialAndFinalObjectsInTheCategoryOfAdjunctions.png 245 × 126; 5 KB
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Isomorphisme d'une catégorie1.png 768 × 614; 12 KB
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Jean Bénabou en 2019.jpg 5,472 × 3,648; 6.36 MB
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Kategória1.png 540 × 266; 4 KB
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Ker-simple.svg 96 × 57; 18 KB
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Ker-simple2.svg 96 × 57; 19 KB
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Kernel of morphism.svg 157 × 106; 13 KB
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Kernel-thm1.svg 126 × 89; 28 KB
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Kernel-thm2-1.svg 55 × 55; 16 KB
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Kernel-thm2-2.svg 55 × 57; 16 KB
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Kernel.svg 106 × 62; 31 KB
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Kleisli Category - morphism composition.png 1,266 × 1,230; 87 KB
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Kleisli Category - morphism composition.svg 1,266 × 1,230; 116 KB
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Kompositiongundf.png 295 × 151; 7 KB
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Lax monoidal funct assoc.png 364 × 199; 8 KB
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Left Unit Coherence of Tensorial Strengths.svg 151 × 64; 29 KB
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LiftingProperties.png 106 × 112; 2 KB
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List object definition.svg 204 × 78; 21 KB
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Mappings-as-moduli.png 286 × 100; 4 KB
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Minoid.png 860 × 188; 24 KB
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Model category lifting.png 96 × 96; 4 KB
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Model category retract.png 158 × 119; 7 KB
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MonadDistrEtaPString.svg 154 × 69; 9 KB
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MonadDistrMuPString.svg 179 × 84; 11 KB
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Monoid multiplication.svg 550 × 138; 17 KB
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Monoid unit svg.svg 363 × 125; 24 KB
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Monoidal category pentagon.svg 921 × 142; 30 KB
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Monoidal category triangle.svg 425 × 142; 26 KB
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Monoidal Coherence Map from Applicative Formulation.svg 436 × 76; 86 KB
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Monoidal natural transformation multiplication.svg 313 × 150; 26 KB
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Monoidal natural transformation unit.svg 238 × 150; 20 KB
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Monoidal2.svg 357 × 121; 21 KB
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Monomorphism pullback square.png 336 × 276; 10 KB
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Monomorphism scenarios.svg 340 × 50; 16 KB
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Morphism-Composition.svg 213 × 26; 8 KB
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Morphism.svg 113 × 26; 5 KB
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MorphismInTheCategoryOfAdjunctions.png 248 × 127; 4 KB
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Natural Transformation between two functors.svg 360 × 155; 28 KB
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Natural transformation diagram.svg 360 × 155; 28 KB
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Natural transformation.svg 125 × 101; 29 KB
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OperadTreeCompose2.svg 200 × 200; 4 KB
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OperadTreeCompose3.svg 200 × 200; 7 KB
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OperadTreeCompose5.svg 200 × 200; 5 KB
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OperadTreeCompose6.svg 200 × 200; 7 KB
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Opposite group nature.svg 250 × 144; 18 KB
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Pentagonal diagram for monoidal categories.svg 827 × 169; 29 KB
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Prod chain.svg 400 × 250; 18 KB
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Projective object.svg 87 × 69; 11 KB
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PullbackS.PNG 416 × 312; 6 KB
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Pure Operator By Tensorial Strength.svg 251 × 71; 44 KB
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Quasifibration-via-hofibre.svg 2,183 × 609; 10 KB
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Quiver Morphism Start Diagram.svg 79 × 65; 27 KB
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Quiver Morphism Target Diagram.svg 79 × 65; 27 KB
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Relations category op.svg 213 × 213; 100 KB
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Relations category.svg 213 × 213; 96 KB
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RetractOfMorphism.png 189 × 91; 1 KB
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Right Kan extension universal property diagram.PNG 195 × 99; 2 KB
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Right Kan Extension.png 175 × 106; 5 KB
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Sample Bratteli diagram.svg 186 × 86; 23 KB
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Section (théorie des catégories).png 768 × 614; 13 KB
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Simple category.svg 200 × 200; 960 bytes
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Slice category.png 276 × 285; 10 KB
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Smart Plant.jpg 3,825 × 2,381; 1.16 MB
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Stone functor.svg 390 × 177; 37 KB
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String diagram adjunction.svg 314 × 144; 16 KB
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String diagram counit.svg 90 × 81; 10 KB
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String diagram identity.svg 71 × 109; 5 KB
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String diagram unit.svg 114 × 81; 11 KB
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Strong monad associative.svg 700 × 165; 33 KB
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Strong monad commutation.png 563 × 213; 10 KB
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Strong monad commutation.svg 563 × 168; 31 KB
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Strong monad left unit.svg 288 × 150; 26 KB
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Strong monad multiplication.svg 550 × 165; 30 KB
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Strong monad unit.svg 288 × 145; 25 KB
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SubobjectClassifier-03.png 110 × 126; 961 bytes
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Symmetric monoidal associativity coherence.png 547 × 355; 18 KB
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Symmetric monoidal category swap.svg 36 × 27; 1 KB
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Symmetric monoidal inverse law.png 493 × 201; 9 KB
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Tensorial Costrength By Tensorial Strength.svg 164 × 76; 48 KB
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Tensorial Strength By Functor Strength.svg 416 × 76; 90 KB
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Tensorial Strength By Pure Operator.svg 311 × 74; 53 KB
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TermAlgebra-Diagram-01.svg 79 × 61; 16 KB
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Terminal and initial object.svg 640 × 344; 3 KB
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Trace diagram associativity.svg 700 × 250; 39 KB
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Trace diagram dinaturality.svg 700 × 250; 35 KB
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Trace diagram naturality 1.svg 700 × 250; 35 KB
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Trace diagram naturality 2.svg 700 × 250; 35 KB
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Trace diagram superposition.svg 700 × 250; 40 KB
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Trace diagram vanishing.svg 700 × 250; 24 KB
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Trace diagram yanking.svg 700 × 250; 20 KB
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Transitive-closure.svg 1,063 × 567; 6 KB
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Trasfnat composizione orizzontale elem kf.png 690 × 398; 19 KB
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Trasfnat composizione orizzontale kf.png 479 × 269; 11 KB
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Trasfnat composizione verticale kf.png 318 × 165; 6 KB
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Trasformazione naturale kf.png 420 × 204; 8 KB
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Uinit-counit-1.png 212 × 147; 4 KB
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Unit-counit.png 489 × 162; 11 KB
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Universal morphisms appear as the unit and counit of adjunctions.svg 524 × 156; 32 KB
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Universal-property-products.svg 259 × 84; 29 KB
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Vertical composition of natural transformations.svg 1,760 × 605; 17 KB
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Waldhausen cat.png 160 × 144; 4 KB
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