153:
696:
690:
165:
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757:
297:
292:
800:
320:
450:
228:
417:
365:
346:
525:
467:
145:
90:
514:
198:
are respectively the associativity, the left identity and the right identity of the monoidal category
479:
409:
387:
171:
369:
316:
305:
777:
753:
280:
175:
75:
376:
331:
301:
276:
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336:
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501:
has a monoidal structure induced by the composition and the identity
284:
28:
528:, every object becomes a comonoid object via the diagonal morphism
726:
772:
Kilp, Mati; Knauer, Ulrich; Mikhalov, Alexander V. (2000).
474:(again, with the tensor product), is a unital associative
752:(4th corr. print. ed.). New York: Springer-Verlag.
311:
A monoid object in the category of monoids (with the
549:. Dually in a category with an initial object and
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524:For any category with a terminal object and
300:(with the monoidal structure induced by the
279:(with the monoidal structure induced by the
553:every object becomes a monoid object via
750:Categories for the working mathematician
729:, the category of monoids acting on sets
739:
685:In other words, the following diagrams
708:and their monoid morphisms is written
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326:A monoid object in the category of
223:Suppose that the monoidal category
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298:category of topological spaces
1:
811:Categories in category theory
482:, and a comonoid object is a
774:Monoids, Acts and Categories
748:Mac Lane, Saunders (1988).
704:The category of monoids in
513:. A monoid object in is a
451:differential graded algebra
443:category of chain complexes
827:
366:category of abelian groups
328:complete join-semilattices
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806:Objects (category theory)
186:is the unit element and
621:in a monoidal category
497:, the category of its
321:EckmannāHilton argument
209:in a monoidal category
159:and the unitor diagram
144:such that the pentagon
315:of monoids) is just a
776:. Walter de Gruyter.
585:Categories of monoids
382:, a monoid object in
801:Monoidal categories
642:morphism of monoids
458:A monoid object in
410:category of modules
342:A monoid object in
290:A monoid object in
287:in the usual sense.
269:A monoid object in
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589:Given two monoids
317:commutative monoid
306:topological monoid
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281:Cartesian product
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221:
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216:
215:dual category
212:
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499:endofunctors
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468:category of
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244:commutative
234:. A monoid
40:mathematics
795:Categories
734:References
561:⊔ id
205:Dually, a
701:commute.
488:coalgebra
98:morphisms
721:See also
630: :
571:⊔
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536: :
436:-algebra
421:-algebra
337:quantale
304:), is a
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264:Examples
229:symmetry
207:comonoid
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480:algebra
432:graded
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118:called
56:algebra
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