142:
685:
679:
154:
799:
794:
770:
746:
286:
281:
789:
309:
439:
217:
406:
354:
335:
514:
456:
134:
79:
503:
187:
are respectively the associativity, the left identity and the right identity of the monoidal category
468:
398:
376:
160:
358:
305:
294:
766:
742:
269:
164:
64:
365:
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290:
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678:
487:
420:
416:
316:
28:
153:
539:
476:
324:(with the monoidal structure induced by the Cartesian product) is a unital
325:
86:
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490:
has a monoidal structure induced by the composition and the identity
273:
17:
517:, every object becomes a comonoid object via the diagonal morphism
715:
761:
Kilp, Mati; Knauer, Ulrich; Mikhalov, Alexander V. (2000).
463:(again, with the tensor product), is a unital associative
741:(4th corr. print. ed.). New York: Springer-Verlag.
300:
A monoid object in the category of monoids (with the
538:. Dually in a category with an initial object and
8:
513:For any category with a terminal object and
289:(with the monoidal structure induced by the
268:(with the monoidal structure induced by the
542:every object becomes a monoid object via
739:Categories for the working mathematician
718:, the category of monoids acting on sets
728:
674:In other words, the following diagrams
697:and their monoid morphisms is written
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315:A monoid object in the category of
212:Suppose that the monoidal category
163:. In the above notation, 1 is the
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16:For the algebraic structure, see
683:
677:
152:
140:
308:. This follows easily from the
287:category of topological spaces
1:
800:Categories in category theory
471:, and a comonoid object is a
763:Monoids, Acts and Categories
737:Mac Lane, Saunders (1988).
693:The category of monoids in
502:. A monoid object in is a
440:differential graded algebra
432:category of chain complexes
816:
355:category of abelian groups
317:complete join-semilattices
15:
795:Objects (category theory)
175:is the unit element and
610:in a monoidal category
486:, the category of its
310:EckmannāHilton argument
198:in a monoidal category
148:and the unitor diagram
133:such that the pentagon
304:of monoids) is just a
765:. Walter de Gruyter.
574:Categories of monoids
371:, a monoid object in
790:Monoidal categories
631:morphism of monoids
447:A monoid object in
399:category of modules
331:A monoid object in
279:A monoid object in
276:in the usual sense.
258:A monoid object in
202:is a monoid in the
578:Given two monoids
306:commutative monoid
295:topological monoid
85:together with two
735:Section VII.3 in
540:finite coproducts
482:For any category
270:Cartesian product
165:identity morphism
65:monoidal category
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733:
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291:product topology
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461:-vector spaces
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729:
722:
717:
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647:
643:
639:
636:
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634:
632:
626:
622:
618:
614:, a morphism
613:
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603:
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591:
587:
583:
573:
567:
563:
559:
554:
548:
541:
536:
532:
528:
523:
516:
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509:
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470:
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284:
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256:
252:
250:
247:
243:
239:
234:
230:
226:
222:
219:
215:
210:
208:
205:
204:dual category
201:
197:
192:
190:
186:
182:
178:
174:
170:
166:
162:
155:
151:
150:
149:
143:
139:
138:
137:
136:
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110:
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84:
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37:monoid object
34:
30:
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731:
702:
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692:
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581:
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565:
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498:
494:
488:endofunctors
483:
472:
464:
458:
457:category of
452:
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381:
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233:commutative
223:. A monoid
29:mathematics
784:Categories
723:References
550:⊔ id
194:Dually, a
690:commute.
477:coalgebra
87:morphisms
710:See also
619: :
560:⊔
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425:-algebra
410:-algebra
326:quantale
293:), is a
272:), is a
253:Examples
218:symmetry
196:comonoid
492:functor
469:algebra
421:graded
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107:called
45:algebra
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382:Mod
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